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Journal of Mathematics
Volume 2016, Article ID 1706812, 5 pages
http://dx.doi.org/10.1155/2016/1706812
Research Article

Graphs Generated by Measures

A. Assari1,2 and M. Rahimi1,2

1Department of Basic Science, Jundi-Shapur University of Technology, Dezful, Iran
2Department of Mathematics, Faculty of Science, University of Qom, Qom, Iran

Received 28 July 2016; Revised 9 October 2016; Accepted 20 November 2016

Academic Editor: Ali Jaballah

Copyright © 2016 A. Assari and M. Rahimi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper, a graph is assigned to any probability measure on the -algebra of Borel sets of a topological space. Using this construction, it is proved that given any number (finite or infinite) there exists a nonregular graph such that its clique, chromatic, and dominating number equals .