Let G be a simple connected graph with exactly 8 vertices, one of them has degree 7, and the other 7 vertices have degree 3. Is G isomorphic to W-? Justify your answer.

Q: 5. Let G = (V, E) be a finite, connected graph. Show that if no vertex of G has degree less than 2,…

A:

Q: Let G be a simple graph with 15 vertices and 4 connected components. Prove that G has at least one…

A:

Q: Prove that if G is a graph with no isolated vertices, then α'(G) +β'(G) = n(G)

A: Here α'(G) is largest size of matching in G. β'(G) is the smallest size of an edge cover. We have to…

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: 11. Prove: If G is a simple connected graph where the average degree of the vertices is exactly 2,…

A:

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: 18. Let G be a graph with n vertices and exactly n-1 edges . Prove that G has either a vertex of…

A: Now, we need to prove that if G is a graph with n vertices and (n-1) edges then G has either a…

Q: Use Ore's theorem to prove that any n-vertex graph G for which |E(G)|> (",') +2 is Hamiltonian.

A: answer is in next step

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: Let G =(V,E) be a finite graph on n ≥ 3

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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: Let G be a planar graph in which every face is either a triangle or a pentagon. If G has 12…

A: It is given that Let G be a planar graph in which every face is either a triangle or a pentagon. If…

Q: Let G be a simple graph with n vertices, which is regular of degree d. By considering the number of…

A:

Q: (b) Give an example of a disconnected simple graph on n vertices in which every vertex has degree…

A: We need to give an example of a disconnected simple graph on n vertices in which every vertex has…

Q: 37. Consider Graph A and B are isomorphic. If vertex E of Graph A corresponds to vertex 2 in Graph…

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Q: Let G be a connected simple graph in which all vertices have degree 4. Prove that it is possible to…

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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: Prove that every graph G on {1,... n} which is acyclic and has n 2 edges has exactly 2 connected…

A: Given: To prove the given statement as follows:

Q: 3. A labeled Ks graph with labeled edges appears below. Which edge permutation is induced by the…

A: Solution:

Q: Let G be a graph on n vertices (with no loops or multiple edges). Prove that if all vertices in G…

A: 1. A graph G is an ordered pair (V(G), E(G)) consisting of a non-empty set V(G) of vertices and a…

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: Suppose that G is a k-regular graph of n vertices, and m edges. The vertex connectivity of G is…

A: Sol

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: Prove or disprove: There exists some n > 1 such that there is a simple graph on n vertices, where…

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Q: 11. > Prove: If G is a simple connected graph where the average degree of the vertices is exactly 2,…

A:

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: 4. Is the following graph strongly connected? If not, is it weakly connected? 1

A: Digraph: strongly and weakly connected

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

A:

Q: [1] Write down the vertex-connectivity K(G) and the edge-connectivity 2(G) for each of the following…

A: Vertex connectivity: The minimum number of vertices required to disconnect the graph G is called…

Q: Show that every simple graph on n vertices is isomorphic to a subgraph of Kn.

A: We need to prove that every simple graph on n vertices is isomorphic to a subgraph of Kn (complete…

Q: Show that it is not possible to creak graph the" degree with g vertices such that every a of vertex…

A: Given that  The no of vertices = 9 degree of each vertices =3 To show such graph is not possible.

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: Let G be a connected graph of order n = 4 and let k be an integer with 2 ≤ k ≤ n − 2. Prove that if…

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Q: Prove : for r belongs to Z+, every r connected graph on an even number of vertices with no induced…

A:

Q: Let G be a graph with n vertices and an independent set of size s ≥ 1. What is the maximum possible…

A: Please check the next step for details

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

A: Consider G be a simple connected graph with exactly 8 vertices, one of them has degree 7, and…

Q: Prove that in any simple graph G with n vertices and m edges, 2m ≤ n^2 − n.

A: We need to prove that in any simple graph G with n vertices and m edges, 2m≤n2−n

Q: Draw a single graph G which satisfies all of the following properties. - All vertices of G are of…

A:

Q: Let A and B each be sets of N labeled vertices, and consider bipartite graphs between A and B. Show…

A: Consider two sets Aand B with N labelled vertices and bipartite graphs between Aand B. Show by…

Q: Let G be a simple graph with 20 vertices. Suppose that G h ponents, and every pair of distinct…

A: Given: Simple graph G with 20 vertices. G has two-component with distinct vertices that satisfy…

Q: Let G be a graph with v vertices and e edges. Let M be the maximum degree of the vertices of G, and…

A: We are given a G graph G with v number of vertices and e number of edges in the graph. we are also…

Q: Prove that if G is a graph of order p and has size greater than ¹) then G is connected. 2

A:

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: Let A and B each be sets of N labeled vertices, and consider bipartite graphs between A and B. How…

A: Given : Let A and B each be sets of N labeled vertices, and consider bipartite graphs between A and…

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…

Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.