16. Let G be a graph with n vertices , t of which have degree K and the others have degree K+1 ,prove that t = (K+1)n-2e , e is number of edges in G .

Q: Compute the vertex set V and edge set E of the graph G = (V, E) whose Prufer Code is (3, 3, 3,3,…

A: If the prufer code for a graph has length n, then the graph has n+2 vertices. The prufer code for…

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

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Q: 4. Prove: "Show that the number of edges in a simple planar graph of order n is at most 3n – 6".…

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Q: 29. Let G be a graph with vertex set VG and edge set Ec. Let V C VG and EC EG. Is there always a…

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Q: 5. Prove or disprove: Let l', and I; be two simple graphs; with V(T)| = m, E(T)=p.V(T)| =n, E(T2)| =…

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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) Draw graph G with vertex set V (G) = {V₁, V2, V3, V4, V5, V6, V7} and edge set E (G) = {V₁V4, V₁…

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Q: 6. A vertex v of G is essential if v is covered by every maximum matching in G. That is, a'(G - v) =…

A: Given: Here the given vertex v of G is essential if v is covered by every maximum matching in G.…

Q: B\ Prove that " there is no simple graph on four vertices, three of whic have degree 3 and the…

A: To prove: There is no simple graph on four vertices, three of which have degree 3 and the remaining…

Q: For each of the graphs :(i) Find all edges that are incident on y1.(ii) Find all vertices that are…

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Q: Consider a graph G with k vertices and m edges. Show that G has at least one vertex of degree at…

A: To prove that a graph G with k vertices and m edges has at least one vertex of degree at most 2, we…

Q: -nsider the following graph G(V, E) w • The set of vertices V: {2,3, 4, 6, 8, • The set of edges E:…

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