A certain graph G of order n and size m = 17 has one vertex of degree 1, two vertices of degree 2, one vertex of degree 3, and two vertices of degree 5. The remaining vertices of G have degree 4. What is n?

Q: 5. Prove that every graph of order 6 with chromatic number 3 has at most 12 eges.

A: Solution :- As per guidelines.i solve 5th number.

Q: How many vertices do the following graphs have if they contains a) 16 edges and all vertices of…

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Q: A simple graph G on n vertices with m edges is overfull if m> [n/2]A. Show that if G is overfull,…

A: Given that: A simple graph G on n vertices with m edges is overfull if m>n2△. The objective is to…

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A: Given a graph representing H. Statement: If H has at least one vertex of degree greater than zero…

Q: 10. Give an example for each of the following situations, or explain why they cannot happen: (a) A…

A: a) A simple graph on four vertices with total degree 2.b) A simple graph whose vertices all have…

Q: A graph is Euler if * (d) It contains an Euler walk. (b) Its disconnected and every vertex has even…

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Q: Draw the simple undirected graph described below: a) K8 b) Euler graph of order 3.

A: Draw the simple undirected graph described below: a) K8 b) Euler graph of order 3. c)Hamilton graph…

Q: 15. (a) Suppose a graph has 5 vertices and 7 edges, and every vertex has degree 2 or 3. How many…

A: The handshaking theorem states that the sum of the degrees of all vertices in a graph is twice the…

Q: Draw a simple graph (or argue why one cannot exist) that (a) has 6 vertices, 12 edges, and is…

A: (a)Such a graph is not possible as we can seeK3 has 3 vertices 3 edgesK2 has 2 vertices and 1 edgeK4…

Q: 4.1.3. (-) Let G be an n-vertex simple graph other than Kn. Prove that if G is not k-connected, then…

A: Given: Let G be an n-vertex simple graph other than Kn. Prove that if G is not k-connected, then G…

Q: Consider the 4-vertex graph G associated with the Seven Bridges of Königsberg problem from the…

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Q: a) Show that if G is a simple graph with n vertices (where n is a positive integer) and each vertex…

A: Part(a): G is a simple graph with n vertices and degree of each vertex in G is at least n-12. We…

Q: The graph G1 has 5 vertices, all of degree 2. How many edges does G1 have? The graph G2 has 8…

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Q: Find the number of connected components for each of the following graphs. (a) A graph with 8…

A: (a) Given a graph with 8 vertices and 6 edges is shown. Vertex a is connected to vertex b and to…

Q: Prove that for every odd n ≥ 5 there exist a graph of n+1 vertices n of which have degree 3, and the…

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Q: How many edges are there in a graph with 10 vertices each of degree six

A: The sum of degrees of vertices is, 6×10=60. Handshaking theorem: Let G=V.E is an undirected graph…

Q: 3) Draw three non-isomorphic graphs of order 5 and size 5.

A: Three non isomorphic graphs of order 5 and size 5 are:

Q: Suppose a graph G has 1E-23, sax vertices of degree 4, five vertices of degree 3 and the rest have…

A: Given below the detailed solution.

Q: A graph is Euler if * (c) Its connected and every vertex has odd degree (b) Its disconnected and…

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Q: How many vertices will the following graphs have if they contain: (a) 12 edges and all vertices of…

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Q: 2. Give an example of a graph with at least four vertices, or prove that none exists, such that: (a)…

A: The objective is to give an example of a graph with at leas four vertices, or prove that none…

Q: A K- regular graph is a graph where every vertex has degree K

A: Consider the given information. A graph is hamiltonian if it visits every vertex exactly once except…

Q: 4. Give an example (if it exists) of each of the following: (a) a bipartite graph that is regular of…

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Q: 1. Find a graph with 12 edges having six vertices of degree three and the remaining vertices of…

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Q: 3.7 The complete tripartite graph K, consists of three sets of vertices (of sizes r, s and 1), with…

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Q: (7) A connected Eulerian graph has 3 vertices and 7 edges. Show that if one vertex has degree 8,…

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Q: A graph with 7 vertices and 10 edges is shown. Vertex a is connected to vertex b, to vertex d, and…

A: According to the given information, First it is required to draw the graph from the given…

Q: 2. Prove the following and make a sketch. a) Prove that every Eulerian graph of odd order has three…

A: 1. Since G is connected, every vertex has positive degree. Since G has an Eulerian cycle, every…

Q: The number of edges in a graph with 8 vertices each of degree 5 is 10 O 20 O 7 O 40

A: We have to determine the number of edges in the graph with 8 vertices of degreee 5 .

Q: 14) For each of (a)-(c) below, either draw a graph with the specified properties or else explain why…

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Q: 5. A graph G has 105 vertices of which there are 13 vertices of degree 3, 33 vertices of degree 5…

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Q: Either draw a graph with the specified properties or explain why no such graph exists. Graph with…

A: As 3 questions are given , I will solve only the first question, 1.Graph with five vertices of…

Q: Let H be a simple graph on n vertices that has m edges. Prove that H contains at least m – n +1…

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Q: Let A and B cach be sets of N labeled vertices, and consider bipartite graphs between A and B. 1)…

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Q: Problem 1: find the maximum possible number of edges in ipartite graph of order n for any integer n…

A: The bipartite graph on n vertices with the maximum edges is clearly a complete bipartite graph,…

Q: Suppose G is a connected graph with n > 1 vertices and n − 1 edges. Prove that G has a vertex of…

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Q: Let G be a graph of order 21 and size 50. There are three vertices of degree 2, six vertices of…

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Q: for which values of m and n are km,n regular?

A: Given: A simple graph is called regular if every vertex of this graph has the same degree. A regular…

Q: (a) An undirected simple graph has 1000 vertices of degree 6 and 200 vertices of de- gree 2. This…

A: Since you have posted a multiple question according to guildlines I will solve first  question for…

Q: 1. (a) What is the maximum number of edges that a bipartite planar graph with 10 vertices can have?…

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Q: O For odd values of n>1, Kn is Eulerian. O For odd values of na 1, Kn has an Eulerian trail. ) K2…

A: The above statement is true as “A graph is Eulerian if and only if the degree of each vertex is…

Q: Given the following directed graph G: a. What is the in-degree of vertex 6? b. What is the…

A: This question is related to graphs. This question has 8 sub parts. But according to rules of…

Q: 6. A connected graph with four edges and four vertices has two vertices of degree two. Show that a.…

A: We have given connected graph with four edges and four vertices that has 2 vertices  which having…

Q: 3. Let D be a graph on 25 edges such that there is a vertex of degree 1, a vertex of degree 2, a…

A: We are given graph D on 25 edges. D has a vertex each of degree 1,2,3,4,5,6,7,8,9 respectively.

Q: Let G be graph with 8 vertices and 10 edges. If every vertex of G has degree 2 or 3, then How many…

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Q: 10. Graph How many edges are there in a graph with 8 vertices of degree 5? If a graph has 7…

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Q: a) State the number of edges in the complete graph K9, where each pair of distinct vertices is…

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Q: 6. A connected graph with four edges and four vertices has two vertices of degree two. Show that a.…

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