# chromatic number of graph and adjacency matrix

Please see attached questions.

This is three questions.

Question #1 - find the chromatic number of the graph.

Question #2 - It might be supposed that if a graph has a large number of vertices and

each vertex has a large degree, then the chromatic number would have to be large. Show

that this conjecture is incorrect by constructing a graph with at least 12 vertices, each of

degree at least 3, that is chromatic number 2.

Need Attached Graph in editable format, i.e. xls, doc, etc.

Question #3 - Find the adjacency matrix and adjacency list for the directed graph in the

indicated exercise. Order the vertices according to alphabetical order.

Let S - {1,2,4,8} and R = {(1,8), (2,4), (8,2), (4,1), (2,2), (8,1)} be the relation

defined S. Draw the directed multigraph of this relation. Need Attached Graph in

editable format, i.e. xls, doc, etc.

https://brainmass.com/math/matrices/chromatic-number-of-graph-and-adjacency-matrix-223383

#### Solution Preview

See attached file for diagrams to go along with the solution.

Answer: 1

The chromatic number of a graph is the least number of colors required to do coloring of that graph or more clearly we can say that the chromatic number of a graph G is the smallest number of colors needed to color the vertices of G such that no two adjacent vertices share the same color.

In the given graph, if we color vertex A with ...

#### Solution Summary

Basics of chromatic number of graph, adjacency matrix and list are described.