Question 1. Let G be a graph with at least 2 vertices. Prove or disprove: a) Deleting a vertex of maximum degree cannot increase the average degree. b) Deleting a vertex of minimum degree cannot decrease the average degree.

Use Kuratowski’s theorem to prove that the following graph is not planar.

Explain thoroughly!!

Question 4. Let K, be the complete graph on n vertices. How many edges does it have? Justify your answer.

Construct a graph with vertices J, K, L, M, N whose degrees What is the edge set? "

c) sketch its graph

True or False. Justify Your Answer.  a) There is a vertex v in a bipartite graph G = (V,E) with deg (v) = m+n. Where m = |V1| and n = |V2| b) is it possible for a graph to be a tree and complete bipartite graph at the same time?

What is the minimum number of colors you need to color the vertices of this graph such that if two vertices are adjacent they receive different colors?

The sum of the degree of vertices of a graph is always an even number. O True False

Previo Construct a connected simple graph, that has no circuit, with vertices M, N, 0, P, Q, R, S, T, U such that the degree of O is 4.