If G1 and G2 are isomorphic, must they have the same number of vertices? If G1 and G2 have the same number of vertices must they be isomorphic? If not, give an example.

Q: In a round-robin tournament the Tigers beat the BlueJays, the Tigers beat the Cardinals, the Tigers…

A: Directed graph: A directed graph is a graph in which a set of objects are connected together such…

Q: G = (V, E) has n > 2 vertices and no self-loops, show that there exist two vertices v w ch that…

A: Graph without self loop is called simple

Q: (a) Show that in a simple graph with n > 2 vertices, at least two vertices have the same degree.

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: Let G be a simple connected graph with exactly 8 vertices, one of them has degree 7, and the other 7…

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Q: Prove that there must be at least two vertices with the same degree in a simple graph

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Q: A) Prove the statement: If G is a bipartite graph, then it does not contain cycles of odd length.

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Q: When two graphs G and H are isomorphic, this means: there exists a bijection between the vertices of…

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Q: Let G be a simple graph on 9 vertices, and assume we know that the sum of all degrees in G is at…

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Q: When two graphs G and H are isomorphic, this means: there exists a bijection between the vertices of…

A: Two graphs G and H are said to be isomorphic, if there exist a bijection f between their vertices…

Q: Let G be a graph such that every vertex has degree 4 and the number of edges is 12. How many…

A: Simply keep in mind that vertex degree multiplied by number of vertices is two times number of…

Q: If G1 and G2 are isomorphic, must they have the same number of edges? If G1 and G2 have the same…

A: If G1 and G2 are isomorphic then they must have the same number of edges.But if G1 and G2 have same…

Q: Show that every graph with n vertices and k edges, n> k has n – k components.

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Q: Graphs G and H are said to be isomorphic if the vertices are in one-to-one correspondence and the…

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Q: Suppose that a graph G has n vertices, and all vertices have degree greater than or equal to“,.…

A: Let G be a graph with n vertices. Given that all vertices have degree greater than or equal to n-12.…

Q: Use the Handshaking Lemma to show that a graph G always has an even number of vertices with odd…

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Q: For the graphs shown below, either exhibit an isomorphism between vertex sets or explain why the…

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Q: A graph with four vertices is Hamiltonian if each vertex has a degree of two. True O False

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Q: Two graphs G1 (V1, E1) and G2 = (V2, E2) are equal if and only if O V = V2 and E, = E2. O Vị = V2. O…

A: We know two graphs are equal iff  they have  the same vertex set and the same set of edges. such…

Q: show that if Gòe connected grapht that is mot complete, then contains two vertices u and v such that…

A: This problem is related with graph theory. Here, we have to show that if G is a connected graph that…

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: Total number of hamiltonian circuits of the complete graph K is 24 circuits 12 circuits 48 circuits…

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Q: 2) True or False. Points A and L are corresponding vertices, points B and M are corresponding…

A: Translation is a rule to procure a new image from an old image. Translation includes four different…

Q: Prove or disprove that if G has m edges and n vertices, then the degeneracy of G is at least m

A: Given  be a graph with m edges and n vertices. Required to prove that the degeneracy of G is at…

Q: What are the strongly connected components of the digraph below? Your answer should consist of a…

A: A graph is said to be strongly connected if every vertex is reachable from every other vertex. The…

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A: To find- Which of the following relations represented by the directed graph is symmetric?   Concept…

Q: oblem 11.69. Prove that in any tournament which does not contain a cycle, some vertex beats every…

A: Let D is a tournament which does not contain cycle. we will use a theorem to prove this  Suppose D…

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: Graphs G and H are said to be isomorphic if the vertices are in one-to-one correspondence and the…

A: Graph isomorphism: Two graphs G(V,E) and  G'(V',E') are said to be isomorphic if there exists an…

Q: If a graph G has n vertices, all of which but one have odd degree, how many vertices of odd degree…

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Q: (b) Show that G may not necessarily have three cycle subgraphs by giving an example of a graph G,…

A: Consider the equation

Q: A walk is closed if the first and last vertices of the walk are the same, that is, if you finish at…

A: A walk is closed if the first and last vertices of the walk are the same, that is, if you finish at…

Q: True/False: If the graphs G1 and G2 are isomorphic, and G, is connected, then G2 must be connected…

A: If G1 and G2 are isomorphic , and G1 is connected

Q: Which of the following graphs are bipartite? I

A: A graph is bipartite iff graph does not contains any odd cycle.

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: If G is a graph, then the sum of its vertex degrees is nonnegative and even.

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Q: Prove that cycles are bipartite for an even number of vertexes. But they are not bipartite for the…

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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: If G is a simple graph with at least two vertices. prove that G must contain two or more vertices of…

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Q: Consider a bi-partite graph, B, with two vertex sets of m vertices and n vertices. How many entries…

A: A Bi-partite graph B with vertex set m vertices and n vertices

Q: Let G be a graph with exactly 10 vertices and 27 edges. Suppose that each vertex has degree 3, 5, or…

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Q: 12. If G is a simple graph with vertices a, b, c, d, e and d(a) = d(b) = d(c) = 3 (d = degree), then…

A: Here we apply Hand-shaking lemma for simple graph.

Q: Consider a graph G where the vertices are points (a, b) with integer coordinates, and {(ai, bi),…

A: Given: Let us consider graph G, in which the vertices are integer-coordinated points (a,b), and (ai,…

Q: 8. If the vertices of AACM are A(0, 4), C(0, 0), and M(3, 0) and the vertices of ASCR are S(-4, 0),…

A: Given that, ∆ACM is a triangle which vertices are following, A = (0, 4),   C = (0, 0),    M = (3, 0)…

Q: The subject is discrete math Part III. Determine the number of vertices and edges and find the…

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

A: Note - Acc. to Bartleby guidelines, we are supposed to do only first 3 subparts . If you want more…

Q: 5. The vertices are at (-2, 3) and (4,3) and the length of the conjugate axis is 8. -10 10 7.

A: Let's find.

Q: Are the following directed graphs strongly connected or not? Explain why in detail? 3 4 A

A: A directed graph is said to be strongly connected if there is a path between any pair of vertices in…