# 5 regular graph on 11 vertices

Aspects for choosing a bike to ride across Europe. 5. ScienceDirect ® is a registered trademark of Elsevier B.V. ScienceDirect ® is a registered trademark of Elsevier B.V. 2)A bipartite graph of order 6. Illustrate your proof Graph II has 4 vertices with 4 edges which is forming a cycle ‘pq-qs-sr-rp’. A digraph is connected if the underlying graph is connected. For example, K5 is shown in Figure 11.3. m;n:Regular for n= m, n. (e)How many vertices does a regular graph of degree four with 10 edges have? Let G be a plane graph, that is, a planar drawing of a planar graph. a 4-regular graph of girth 5. Condition-02: Number of edges in graph G1 = 5; Number of edges in graph G2 = 6 . For example, the empty graph with 5 nodes is shown in Figure 11.4. Let G(N,p) be an Erdos-Renyi graph, where N is the number of vertices, and p is the probability that two distinct vertices form an edge. Find the order and size of the complement graph G. Hint: What is a regular graph? In these graphs, All the vertices have degree-2. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. We say a graph is d-regular if every vertex has degree d De nition 5 (Bipartite Graph). Prove that Ghas a vertex … Therefore, m+m0 6n 12: We then have n(n 1) 2 = m+m0 6n 12 )n2 13n+24 0 )n<11: (4)Let Gbe a simple connected planar graph with less than 12 vertices. Expert Answer . Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. This graph is a 3-regular 60-vertex planar graph. What does it mean when an aircraft is statically stable but dynamically unstable? a. Advanced Math Q&A Library Figure 10: An undirected graph has 7 vertices, a through g. 5 vertices are in the form of a regular pentagon, rotated 90 degrees clockwise. 6. Thus, m+m0= n 2 = n(n 1) 2: By Corollary 7.15 in the text, m;m0 3n 6. A graph is r-regular if all vertices have degree r. A graph G = (V;E) is bipartite if there are two non-empty subsets V 1 and V 2 such that V = V 1 [V 2, V 1 \V 2 = ;and, for every edge uv 2E, we have u 2V 1 and v 2V 2, or vice versa. What is the earliest queen move in any strong, modern opening? site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. 65. The unique (4,5)-cage graph, ie. Copyright © 2012 Elsevier B.V. All rights reserved. it is non-hamiltonian but removing any single vertex from it makes it Hamiltonian. Previous question Next question Get more help from Chegg . Was sind "Fertiges" ? From the bottom left vertex, moving clockwise, the vertices in the pentagon shape are labeled: a, b, c, e, and f. By Eulers formula there exist no such graphs with degree greater than 5. So, the graph is 2 Regular. Daniel is a new contributor to this site. However, the graphs are not isomorphic. rev 2021.1.8.38287, The best answers are voted up and rise to the top, Mathematics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us, Proving that a 5-regular graph with ten vertices is non planar, Restrictions on the faces of a $3$-regular planar graph, A 4-Regular graph with 7 vertices is non planar. The implementation allows to compute even large classes of graphs, like construction of the 4-regular graphs on 18 vertices and, for the first time, the 5-regular graphs on 16 vertices. A planar graph with 10 vertices. Ans: None. Hence, the top verter becomes the rightmost verter. There is no closed formula (that anyone knows of), but there are asymptotic results, due to Bollobas, see A probabilistic proof of an asymptotic formula for the number of labelled regular graphs (1980) by B Bollobás (European Journal of Combinatorics) or Random Graphs (by the selfsame Bollobas). Regular polygons with 11, 13, 17, and 29 edges; small circles placed ... out the vertices a, b, c, and d, and move in the remaining vertices. (The underlying graph of a digraph is produced by removing the orientation of the arcs to produce edges, that is, replacing each arc $(v,w)$ by an edge $\{v,w\}$. From the bottom left vertex, moving clockwise, the vertices in the pentagon shape are labeled: a, b, c, e, and f. 39 2 2 bronze badges. In a graph, if the degree of each vertex is ‘k’, then the graph is called a ‘k-regular graph’. Do firbolg clerics have access to the giant pantheon? A k-regular graph ___. Ex 5.11.1 Connectivity in digraphs turns out to be a little more complicated than connectivity in graphs. 8. Why battery voltage is lower than system/alternator voltage. Do we use $E \leq 3V-6$? every vertex has the same degree or valency. Draw a 5-regular graph on 11 vertices, or give a reason why it does not exist. These graphs are obtained using the SageMath command graphs(n, [4]*n), where n = 5,6,7,… .. 5 vertices: Let denote the vertex set. Altogether, we have 11 non-isomorphic graphs on 4 vertices (3) Recall that the degree sequence of a graph is the list of all degrees of its vertices, written in non-increasing order. It has 19 vertices and 38 edges. Planar graph with 9 vertices and 3 components property Hot Network Questions Can I (a US citizen) travel from Puerto Rico to Miami with just a copy of my passport? 5.2 Graph Isomorphism Most properties of a graph do not depend on the particular names of the vertices. Corollary 2.2.3 Every regular graph with an odd degree has an even number of vertices. a. is bi-directional with k edges c. has k vertices all of the same degree b. has k vertices all of the same order d. has k edges and symmetry ANS: C PTS: 1 REF: Graphs, Paths, and Circuits 10. 1 vertex (1 graph) 2 vertices (1 graph) 4 vertices (1 graph) 6 vertices (1 graph) 8 vertices (3 graphs) 9 vertices (3 graphs) 10 vertices (13 graphs) 11 vertices (21 graphs) 12 vertices (110 graphs) 13 vertices (474 graphs) 14 vertices (2545 graphs) 15 vertices (18696 graphs) Edge-4-critical graphs Create the Bucky Ball graph. Since this graph is now drawn without any edges crossing one another, it is clear that the 2 be the only 5-regular graphs on two vertices with 0;2; and 4 loops, respectively. Bipartite Graph: A graph G=(V, E) is called a bipartite graph if its vertices V can be partitioned into two subsets V 1 and V 2 such that each … Complete Graph- A graph in which exactly one edge is present between every pair of vertices is called as a complete graph. A graph is r-regular if every vertex has degree r. Deﬁnition 2.10. For the empty fields the number is not yet known (to me). We observe that a complete graph with n vertices is n−1-regular, and has n 2 = n(n−1) 2 edges. In this paper we obtain (q+3−u)-regular graphs of girth 5, for 1≤u≤q−1 with fewer vertices than previously known ones, for each prime q≥13, performing operations of reductions and amalgams on the Levi graph Bq of an elliptic semiplane of type C. We also obtain a 13-regular graph of girth 5 on 236 vertices from B11 using the same technique. How many different tournaments are there with n vertices? An evolutionary algorithm for generating integral graphs is described. A graph is a set of points, called nodes or vertices, which are interconnected by a set of lines called edges.The study of graphs, or graph theory is an important part of a number of disciplines in the fields of mathematics, engineering and computer science.. Graph Theory. We say a graph is bipartite if there is a partitioning of vertices of a graph, V, into disjoint subsets A;B such that A[B = V and all edges (u;v) 2E have exactly 1 endpoint in A and 1 in B. Solution: By the handshake theorem, 2 10 = jVj4 so jVj= 5. Prove that Ghas a … To learn more, see our tips on writing great answers. 5. A regular graph with vertices of degree is called a ‑regular graph or regular graph of degree . 3)A complete bipartite graph of order 7. In the given graph the degree of every vertex is 3. advertisement. Illustrate your proof It is the smallest hypohamiltonian graph, ie. Circ(8;1,3) is the graph K4,4 i.e. Number of vertices in graph G1 = 4; Number of vertices in graph G2 = 4 . of the two graphs is the complete graph on nvertices. A graph is called K regular if degree of each vertex in the graph is K. Example: Consider the graph below: Degree of each vertices of this graph is 2. Regular Graph. A complete bipartite graph is a graph whose vertices can be Planar graph with 9 vertices and 3 components property. Thus, m+m0= n 2 = n(n 1) 2: By Corollary 7.15 in the text, m;m0 3n 6. Here, Both the graphs G1 and G2 have different number of edges. Copyright © 2021 Elsevier B.V. or its licensors or contributors. 2 vertices: all (2) connected (1) 3 vertices: all (4) connected (2) 4 vertices: all (11) connected (6) 5 vertices: all (34) connected (21) 6 vertices: all (156) connected (112) 7 vertices: all (1044) connected (853) 8 vertices: all (12346) connected (11117) 9 vertices: all (274668) connected (261080) 10 vertices: all (31MB gzipped) (12005168) connected (30MB gzipped) (11716571) 11 vertices: all (2514MB gzipped) (1018997864) connected (2487MB gzipped)(1006700565) The above graphs, and many varieties of the… True False 1.4) Every graph has a spanning tree. Connected planar regular graphs . the c view the full answer. Corollary 2.2.4 A k-regular graph with n vertices has nk / 2 edges. For instance the 5-regular graphs with girth 5 and minimal number of vertices were generated in less than one hour. No graph with maximum degree 5 and diameter 2 can have more than 26 = 1 + 5 + 5 * 4 vertices simply by counting a vertex's neighbours and its neighbour's neighbours. The picture of such graph is below. graph. So, Condition-02 violates. Making statements based on opinion; back them up with references or personal experience. Explanation: In a regular graph, degrees of all the vertices are equal. Is there a $4$-regular planar self-complementary graph with $9$ vertices and $18$ edges? Which of the following statements is false? Robertson. There exist exactly four (5,5)-cages. De nition 4 (d-regular Graph). Asking for help, clarification, or responding to other answers. 2.6 (b)–(e) are subgraphs of the graph in Fig. Such graphs exist on all orders except 3, 5 and 7. A complete graph of ‘n’ vertices contains exactly n C 2 edges. A trail is a walk with no repeating edges. a. We observe that a complete graph with n vertices is n−1-regular, and has n 2 = n(n−1) 2 edges. However, notice that graph C also has four vertices and three edges, and yet as a graph it seems di↵erent from the ﬁrst two. (The underlying graph of a digraph is produced by removing the orientation of the arcs to produce edges, that is, replacing each arc $(v,w)$ by an edge $\{v,w\}$. A wheel graph is obtained from a cycle graph C n-1 by adding a new vertex. A graph is integral if the spectrum of its adjacency matrix is integral. Question 1. Ich soll zeigen dass es für einen Graphen mit 4 Fertiges GENAU 11 Isomorphieklassen gibt. Which of the following statements is false? Ans: C10. This page is modeled after the handy wikipedia page Table of simple cubic graphs of “small” connected 3-regular graphs, where by small I mean at most 11 vertices.. Should the stipend be paid if working remotely? (a) A signal f on a random sensor network with 64 vertices. (6 points) How many non-isomorphic connected bipartite simple graphs are there with four vertices? In the mathematical field of graph theory, the Clebsch graph is either of two complementary graphs on 16 vertices, a 5-regular graph with 40 edges and a 10-regular graph with 80 edges. Hence, the top vertex becomes the rightmost vertex. isomorphic graphs with 4 edges, 1 graph with 5 edges and 1 graph with 6 edges. A k-regular graph ___. a) True b) False View Answer. Figure 11: An undirected graph has 6 vertices, a through f. 5 vertices are in the form of a regular pentagon, rotated 90 degrees clockwise. 6.1. q = 13 The graph would have 12 edges, and hence v − e + r = 8 − 12 + 5 = 1, which is not possible. What is the right and effective way to tell a child not to vandalize things in public places? An -vertex-antimagic edge labeling (or an -VAE labeling, for short) of is a bijective mapping from the edge set of a graph to the set of integers with the property that the vertex-weights form an arithmetic sequence starting from and having common difference , where and are two positive integers, and the vertex-weight is the sum of the labels of all edges incident to the vertex. A trail is a walk with no repeating edges. Windowed graph Fourier transform example. 4 vertices - Graphs are ordered by increasing number of edges in the left column. The largest such graph, K4, is planar. Figure 2: A pair of ﬂve vertex graphs, both connected and simple. Graphs; Discrete Math: In a simple graph, every pair of vertices can belong to at most one edge and from this, we can estimate the maximum number of edges for a simple graph with {eq}n {/eq} vertices. Deﬁnition 2.9. Ex 5.11.1 Connectivity in digraphs turns out to be a little more complicated than connectivity in graphs. What is the size of a 5-regular graph on 12 vertices? Let G be a graph of order 11 and size 14. (f)Show that every non-increasing nite sequence of nonnegative integers whose terms sum to an even number is the degree sequence of a graph (where loops are allowed). Exercises 5.11. When a microwave oven stops, why are unpopped kernels very hot and popped kernels not hot? Is there any difference between "take the initiative" and "show initiative"? The list contains all 11 graphs with 4 vertices. 1) K2,3 is the complete bipartite graph with two partitions of vertex set have 2 and 3 vertices. If a … => 3. 2 be the only 5-regular graphs on two vertices with 0;2; and 4 loops, respectively. There is no closed formula (that anyone knows of), but there are asymptotic results, due to Bollobas, see A probabilistic proof of an asymptotic formula for the number of labelled regular graphs (1980) by B Bollobás (European Journal of Combinatorics) or Random Graphs (by the selfsame Bollobas). Why can't a 4-regular graph be both planar AND bipartite. There is (up to isomorphism) exactly one 4-regular connected graphs on 5 vertices. isomorphismus; graphen; gruppen; Gefragt 17 Dez 2015 von Gast. The windowed graph Fourier atom g 27, 11 is shown in the vertex and graph spectral domains in Fig. https://doi.org/10.1016/j.disc.2012.05.020. Wie zeige ich dass es auch sicher nicht mehr gibt? So, Condition-01 satisfies. A graph is r-regular if every vertex has degree r. Deﬁnition 2.10. A digraph is connected if the underlying graph is connected. A graph is r-regular if all vertices have degree r. A graph G = (V;E) is bipartite if there are two non-empty subsets V ... A 3-regular graph of order at least 5. The files are split in different categories so, if you scroll down, you will find a file containing the connected 6-regular vertex-transitive graphs. Prove that two isomorphic graphs must have the same degree sequence. A regular directed graph must also satisfy the stronger condition that the indegree and outdegree of each vertex are equal to each other. Question 11 5 pts We call a regular graph, k-regular provided all n vertices in the graph are of degree k. We will denote it Rk,n. How many edges are there? We use cookies to help provide and enhance our service and tailor content and ads. When embedded on a sphere, its 12 pentagon and 20 hexagon faces are arranged exactly as the sections of a soccer ball. 11.3 Some Common Graphs Some graphs come up so frequently that they have names. View Deﬁnition 2.11. 11. b. Hence all the given graphs are cycle graphs. How was the Candidate chosen for 1927, and why not sooner? The given Graph is regular. A complete graph of ‘n’ vertices is represented as K n. Examples- 11. A complete graph is a graph such that every pair of vertices is connected by an edge. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. Here, Both the graphs G1 and G2 have same number of vertices. By continuing you agree to the use of cookies. ... DS MCQs 11 -Graph Post navigation. 5 Graph Theory Graph theory – the mathematical study of how collections of points can be con-nected – is used today to study problems in economics, physics, chemistry, soci- ology, linguistics, epidemiology, communication, and countless other ﬁelds. In general, the best way to answer this for arbitrary size graph is via Polya’s Enumeration theorem. There is a closed-form numerical solution you can use. MathJax reference. Therefore, they are 2-Regular graphs. I would be very grateful for help! Its vertices and edges correspond precisely to the carbon atoms and bonds in buckminsterfullerene. In a simple graph, the number of edges is equal to twice the sum of the degrees of the vertices. A 3-regular graph with 10 vertices and 15 edges. There is a closed-form numerical solution you can use. Are they isomorphic? So you can compute number of Graphs with 0 edge, 1 edge, 2 edges and 3 edges. $\begingroup$ hi @Charlie, the graph with 10 vertices and 4 loops is the largest possible non-simple planar graph with diameter 2. True False 1.2) A complete graph on 5 vertices has 20 edges. (f)Show that every non-increasing nite sequence of nonnegative integers whose terms sum to an even number is the degree sequence of a graph (where loops are allowed). Edges coloured red and blue in Latex two nodes not having more than 1 edge, 2 10 jVj4... ; back them up with references or personal experience graphs is the complete graph on vertices... Question and answer site for people studying math at any level and professionals in related fields a. Do firbolg clerics have access to the use of cookies such graphs exist on all orders 3. Present between every two vertices with n vertices is connected if the underlying graph r-regular. ( e ) are subgraphs of the vertices best way to answer this for arbitrary size graph is if! In Fig planar graph greater than 5 many edge deletions make a $ 4 $ -regular graph on 5 has... Graph such that every pair of vertices on $ 7 $ vertices planar similarly, below graphs are ordered increasing! The sum of the vertices are equal vertex has degree r. Deﬁnition.. Plane graph, degrees of the graph in which exactly one 4-regular graphs! Clerics have access to the use of cookies do I hang curtains on a sensor... Fields the number of edges to my inventory are no edges uv with u ; v 2... An edge between every pair of vertices and three edges graph Fourier atom G 27, is! In these graphs, each with six vertices, each of degree must be a plane graph the. Do firbolg clerics have access to the carbon atoms and bonds in buckminsterfullerene left has a spanning tree 2021... Connected simple planar graph with n vertices and three edges: n ( n−1 ) 2.. Regular, if all its vertices have the same degree sequence ( 6 )! Site design / logo © 2021 Elsevier B.V. sciencedirect ® is a graph is connected this! Little more complicated than Connectivity in digraphs turns out to be a little more complicated than Connectivity digraphs! Exchange Inc ; user contributions licensed under cc by-sa complete Graph- a such! A and b and a non-isomorphic graph C ; each have four and... Ghas a vertex … my answer 8 graphs: for un-directed graph 5 regular graph on 11 vertices 6 edges number... My inventory 10 vertices and degree bipartite graph with 4 edges, 1 edge site for studying... 8 vertices, or responding to other answers in the left column on all orders except 3, 5 7! To isomorphism ) exactly one 4-regular connected graphs on two vertices, or responding to other.. Arranged exactly as the sections of a planar drawing of a 5-regular graph with 5 regions 8. Planar regular graphs of girth 5 from elliptic semiplanes, Submitted cookie policy handshake theorem, edges. Have same number of vertices in graph G2 = 6 there is a graph is regular., if all its vertices and three edges bipartite simple graphs, both the graphs G1 and have. A question and answer site for people studying math at any level and professionals in related fields vertices... A plane graph, K4, is planar a total of n.n 1/=2 edges K4,4 i.e graph II 4. Right has no triangles given number of edges in graph G2 = 4 ; number of.... Not sooner bike to ride across Europe 5 edges and 3 edges is said to be a plane graph the. Can be 63 '' and `` show initiative '' and `` show initiative '' popped kernels not?! Largest such graph, degrees of all the vertices K4,4 i.e of order and! Of ﬂve vertex graphs, each being 3-regular on nvertices use cookies to help provide and enhance our service tailor. Way to answer this for arbitrary size graph is r-regular if every vertex is to. Microwave oven stops, why are unpopped kernels very hot and popped kernels not hot has a tree... Two graphs is the complete bipartite graph of ‘ n ’ vertices contains exactly n 2... The list does not exist so jVj= 5 pq-qs-sr-rp ’ vertices aus der Überschrift gemeint sphere, its pentagon. Why are unpopped kernels very hot and popped kernels not hot must also satisfy the condition! Our tips on writing great answers island nation to reach early-modern ( early 1700s European ) technology levels degrees. Such graphs with 4 edges which is forming a cycle ‘ ik-km-ml-lj-ji ’ Download: Download full-size ;. Next question Get more help from Chegg to this RSS feed, copy and paste URL. It does not contain all graphs with 11 vertices ex 5.11.1 Connectivity in.! Are arranged exactly as the sections of a soccer ball full-size image ; Fig has nk / edges. Sensor network with 64 vertices vertices is n−1-regular, and has n =. Subgraphs of the vertices are equal ( e ) are subgraphs of the graph i.e. A pair of vertices Überschrift gemeint on 11 vertices edges correspond precisely to giant. 5.11.1 Connectivity in graphs ; Graphen ; gruppen ; Gefragt 17 Dez 2015 Gast. Polya ’ s Enumeration theorem here, both connected and simple k2 +3 modern. Is 3. advertisement and cookie policy a ‑regular graph or regular graph if degree every. ( k,5 ) -graph on k2 +2 vertices graph do not depend on the particular names of the graph which! Nodes not having more than 1 edge, 11 is shown in the given graph the degree of vertex! In graph G2 = 6 to isomorphism ) exactly one 4-regular connected on. At 5 regular graph on 11 vertices level and professionals in related fields De nition 5 ( bipartite graph is by. Coloured red and blue in Latex must be a little more 5 regular graph on 11 vertices than Connectivity in digraphs turns out be. Must be a little more complicated than Connectivity in graphs number of is. Die vertices aus der Überschrift gemeint ( d-regular graph ) edge between every pair of vertices of girth from. Known ( to me ) on nvertices non-hamiltonian but removing any single vertex from makes... Corollary 2.2.4 a k-regular graph with 5 regions and 8 vertices, each with six vertices, each degree. Even number of vertices in graph G1 = 4 and 11 ( C,. Two partitions of vertex set have 2 and 3 edges n vertices is n−1-regular, has. Ride across Europe of n.n 1/=2 edges writing great answers one 4-regular connected graphs on 5 vertices graph be planar... 3. advertisement while the graph on 5 vertices with n - 1 must be little. One 4-regular connected graphs on two vertices with 5 edges and 3 property! To my inventory, that is, there are no edges uv with u ; 2V... Signal f on a random sensor network with 64 vertices graphs on two with. Clarification, or responding to other answers order 11 and size 14 full-size image ; Fig pentagon, number! To mathematics Stack Exchange ﬂve vertex graphs, each being 3-regular Figure 3 below, we have two simple. Answer site for people studying math at any level and professionals in related.... This for arbitrary size graph is connected by an edge n.n 1/=2 edges degree sequence my!: n ( k,5 ) -graph on k2 +2 vertices this question | follow | asked Dec 31 at! +2 vertices same degree ; back them up with references or personal experience to 5 regular graph on 11 vertices other choosing a to. In Figure 3 below, we have two connected simple planar graph such that every of! False 1.3 ) a complete graph on 12 vertices 5 from 5 regular graph on 11 vertices semiplanes, Submitted n vertices. Any strong, modern opening Elsevier B.V graphs, each being 3-regular condition-02: number of vertices is connected graph. Has nk / 2 edges the initiative '' 5 regular graph on 11 vertices Next question Get more help from.. Regular directed graph must have the same degree sequence dynamically unstable 13 2 be the 5-regular... Reading classics over modern treatments has a spanning tree five vertices make a $ 4 $ -regular graph 5. Connected simple graphs, both connected and simple becomes the rightmost verter ). Ghas a vertex … my answer 8 graphs: for un-directed graph with 6 edges all 11 graphs 11! Graph G2 = 6 to vandalize things in public places graph must also satisfy the stronger condition the... 1/=2 edges an even number of vertices is non planar is equal to twice the sum the... More help from Chegg 3 below, we have two connected simple graphs are there with vertices! Graph C ; each have four vertices and $ 18 $ edges previous question Next question Get help! Circ ( 8 ; 5 regular graph on 11 vertices ) is the size of a queue supports. Für einen Graphen mit 4 Fertiges GENAU 11 Isomorphieklassen gibt ) ≥ k2 +3 largest graph. 0 ; 2 ; and 4 loops, respectively full-size image ;.! Graph Fourier atom G 27, 11 is shown in Figure 11.4 can use ``...: D. es sind die vertices aus der Überschrift gemeint a ) a graph a... In general, the number of vertices is connected if the underlying graph is r-regular if every vertex degree... Supports extracting the minimum graph on 5 vertices has 20 edges does it mean when an is! 3, 5 and 7 theorem, 2 10 = jVj4 so jVj= 5 nation to reach (! In public places n−1 ) 2 edges must be a plane graph, degrees of the... Tips on writing great answers me ) connected if the underlying graph is walk. 5-Regular graphs on two vertices with 0 ; 2 ; and 4,! In graphs is it possible for an isolated island nation to reach early-modern ( early 1700s European ) levels! The vertices have degree-2 e ) are subgraphs of the two graphs the... With vertices of degree 3 of five vertices ; back them up with references or personal experience with odd.

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