Purchase Solution

chromatic number of graph and adjacency matrix

Not what you're looking for?

Ask Custom Question

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.

Purchase this Solution

Solution Summary

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

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 ...

Purchase this Solution

Free BrainMass Quizzes
Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Probability Quiz

Some questions on probability

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.