Let G be a graph with v vertices and e edges. Let M be the maximum degree of the vertices of G, and let m be the minimum degree of the vertices of G. Show that  2e/v≥m

Consider a graph G where the vertices are points (a, b) with integer coordinates, and {(ai, b;), (aj, b;)} is an edge whenever a; + aj = b; + b;. Show that G is bipartite if and only if it has at most two vertices on the line y = x.

Suppose a graph G has the following Harmiltonian Cycle: BAGDFHEJKXB a. How many vertices does G have? b. What is the length of the cycle? C Find two distinct paths between D'and X (distinct means they use different edges) Type your answer in the space provided. For the toolbar, press ALT+F10 (PC) or ALT +FN+F10 (Mac).

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