Discrete Mathematics

Let G be a 5-regular graph with ten vertices. Prove that G is nonplanar.

The faces of a planar p-regular graph are all triangles

The faces of a planar p-regular graph are all triangles (that is each face has degree three). Determine, with proof, the values of p for which this is possible. (Remember a p-regular graph has all vertices of degree p).

Discrete Structures - Define and Prove

Use words to describe the solution process. No programming. 1. (a) Define a tree. (b) Define a bipartite. (c) Prove the following: Every tree is a bipartite.

Chromatic Number; Planar

Use words to describe the solution process. No programming. 2. Let G = (V,E) be a graph where V {1,2,3,4,5,6,7,8,9,10,11,12} and E contains all edges connecting to vertices a and b such that ab=0 (mod 3). What is the chromatic number of G? Is G planar?

discrete f3

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