Draw all nonisomorphic simple graphs with four vertices and no more than two edges.

Q: How many pairwise non-isomorphic connected simple graphs are there on 6 vertices which contain two…

A: We have to find that how many pairwise non-isomorphic connected simple graphs are there on 6…

Q: A trail is a walk that does not repeat an edge. Prove that a trail that repeats a vertex must…

A: Assume that vertex Vk is repeated Let the trail be W: V1V2.....Vk........Vn....Vi.....Vk.......Vj…

Q: Show that the maximum number of edges in a graph with n-vertices is *C2 (d)

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Q: Prove that having n vertices, where n is a positive integer, is an invariant for graph isomorphism.

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Q: Discrete math. Graph theory

A: It is required to draw al, the pairwise non-isomorphic graphs with exactly 5 vertices and 4 edges.

Q: Define maximum number of edges in a simple connected graph with n vertices.

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Q: Show that the graph is 2-colorable by finding a 2-coloring. If the graph is not 2-colorable, explain…

A: A graph is said to be 2-colorable if we can color the vertices in such a way that its vertices are…

Q: When n = 3, there are nonisomorphic simple graphs.

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Q: . How many nonisomorphic directed simpe graphs are there with 4 vertices?

A: According to the given information, it is required to find number of non-isomorphic directed simple…

Q: Show that any graph with two or more nodes and no self-loops contains two nodes that have equal…

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Q: Give an example of a graph with an infinite number of vertices and an infinite number of edges that…

A: A graph consisting of infinite number of vertices and edges is called as an infinite graph.

Q: Give an example of a bipartite graph on 10 vertices that is (a) 2-regular; (b) 3-regular; (c)…

A: (a) 2-regular (b) 3-regular

Q: Show that if a simple graph G has n vertices and at least n edges, then G must contain a cycle.

A: We have to Show that if a simple graph G has n vertices and at least n edges, then G must contain a…

Q: show that a simple planar connected graph with 17 edges and ten vertices cannot be properly colored…

A: We can solve this using Euler theorem

Q: Draw an undirected graph that has exactly 11 edges and at least 5 vertices, in which two of the…

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Q: Draw a bipartite graph with a vertex partition into the two sets {v1, v2, v3, v4} and {v5, V6, v7}…

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Q: hich graph appears to contain all the orderad pairs in this rolation?

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Q: Show that a finite simple graph with more than one vertex has at least two vertices with the same…

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Q: Prove that a graph with at least three vertices is connected if and only if at least two of the…

A: A graph G is a pair of sets V and E where the elements of the non empty set V are called the…

Q: (16) Give an example of two nonisomorphic 2-regular graphs of the same order and show that they are…

A: Isomorphism of two graph:Let, G1 and G2 be two graph . ThenG1 and G2 are said to be isomorphismif ∃…

Q: Let n be a positive integer. Show that every connected graph on n vertices has at least n – 1 -…

A: This is a problem of Graph Theory.

Q: 5. Determine whether the given pair of graphs is isomorphic. u2 v2 V3 V4

A: The number of vertices in graph 1= 8 The number of vertices in graph 2 = 8  The number of vertices…

Q: If you claim that the graphs are isomorphic, show a bijection and show that your bijection preserves…

A: First graph has a cycle of length 3 which is a-b-j-a

Q: Let G be a simple connected plane graph with 6 vertices. (a) (b) (c) (d) What is the largest number…

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Q: Are the following graphs isomorphic? Justify..

A: We clearly see that the first graph, say G1 contains two 3-cycles [one the smaller inside and the…

Q: Draw every simple graph with five vertices and four edges (isolated vertices are allowed) p to…

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Q: Let G be a graph with 10 vertice and 5 components. If a vertex is removed from G, the number of…

A: Answer: 9 and 4

Q: Write an example of three graphs (each with 4 vertices), two of them are isomorphic and two are…

A: We will draw three graphs on four vertices among which two are isomorphic and two are non…

Q: Show that any connected simple planar graph on n vertices must have at most n/2 vertices of degree…

A: Consider the equation

Q: True or False: The edge set of every closed trail in a graph can be partitioned into edge sets of…

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Q: 3 5

A: Isomorphism of graph: Let G and H be two graphs. They are said to be isomorphic if there exists a…

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: True or false: If a connected graph G can be decomposed into exactly k paths then exactly 2k…

A: To Prove: A connected graph can be decomposed into exactly k paths then exactly 2k vertices of G…

Q: State whether the following statement is true or false. Justify your answer with a short proof or a…

A: Consider the general case, Let G be k-edge connected graph then we shall rove that G is k connected.…

Q: Draw a graph with two loops around vertex e, with end vertices a and f, with multiple edges on…

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Q: 3) Show by example that there is a bipartite graph between A and B with N² – N edges, and no perfect…

A: For any queries please le me know through comments. I will try to reply ASAP! Please Thumbs up if…

Q: B: Fined the dual graph for Jollowing graphs the

A: Given

Q: Can a simple graph exist with 9 vertices all of degree 5?

A: Handshaking lemma: In any graph, sum of degree of all the vertices is twice the number of edges…

Q: Are the following 2 graphs isomorphic? Discuss your answer with appropriate reasoning.

A: Given two graphs. From the first graph, d(u1)=3d(u2)=3d(u3)=2d(u4)=2d(u5)=3d(u6)=3

Q: Let G be a connected graph with at least two nodes. Prove that it has a node such that if this node…

A: Consider a connected graph with at least two vertices. choose vertices u,v so that du,v=maximum if…

Q: Draw all subgraphs of this graph

A: Given: There are 3 vertices, hence there will be 23=8 sub graphs Graph nodes: Nodes is defined as…

Q: Write an example of three graphs (each with 4 vertices), two of them are isomorphic and two are…

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Q: (!) Let G be a graph whose odd cycles are pair wo odd cycles in G have a common vertex. Prove

A: Given : Graph G has odd cycles that are pair-wise intersecting, i.e, every two odd cycles in G has a…

Q: 3. Find the degree of the vertices of the following graphs and verify the handshaking theorem.

A: Degree of a vertex is the number of edges incident on it.

Q: draw all nonisomorphic simple graphs with four vertices and no more than two edges

A: Given: Four vertices and two edges. To sketch: All non-isomorphic simple graphs no more than two…

Q: Select all the graphs that are trees. B.

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Q: What is a(G) if G is a complete graph on n vertices?

A: It is given that G is a complete graph on n vertices. Also provided are some basic definitions about…

Q: Find a self-complementary graph with 8 vertices.

A: We know the definition of Complement of a graph, The complement of a graph G is a graph G' on the…