Explore BrainMass
Share

Graph coloring; chromatic number of graph

This content was STOLEN from BrainMass.com - View the original, and get the already-completed solution here!

The three questions are stated in an attached .doc file (1.doc).

In part 1, a diagram is given, and whether the object depicted in the diagram is a graph is to be determined.

In part 2, a graph is given and its chromatic number is to be determined.

In part 3, a graph is given and the number of colors needed to color the regions of the graph (to ensure that adjacent regions have different colors) is to be determined.

© BrainMass Inc. brainmass.com October 24, 2018, 9:30 pm ad1c9bdddf
https://brainmass.com/math/graphs-and-functions/graph-coloring-chromatic-number-of-graph-128936

Attachments

Solution Preview

Complete solutions are given in an attached .doc file (1-Solution.doc).

In part 1, it is determined that the objected depicted in the given diagram is a graph; its vertex set and edge set are presented.

In part 2, the definition of chromatic ...

Solution Summary

The question of whether the object depicted in the given diagram in part 1 is a graph is answered. A detailed determination of the chromatic number of the graph in part 2 is presented, as is a detailed determination of the number of colors needed in part 3 (to ensure that adjacent regions have different colors). The definition of chromatic number of a graph is reviewed.

$2.19
See Also This Related BrainMass Solution

Question on chromatic number of graph, adjacency matrix and list.

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.

View Full Posting Details