Chromatic number of graphs with special distance sets-III
Abstract
An integer distance graph is a graph G(Z;D) with the set of integers as vertex set and an edge joining two vertices u and v if and only if| u − v |∈ D where D is a subset of the positive integers. It is known that(G(Z; P)) = 4 where P is a set of Prime numbers. In this paper we have consideredthe open problem of characterizing class three sets when the distanceset D is not only a subset of primes P but also a special class of primes like Markov primes, Bell primes, Dihedral primes, Mills primes, Ramanujan primes,Quartan primes, Isolated primes and Thabit Number primes. We also indicatealternative formulations for a prime distance graph and raise certain open problems.
Copyright © 2012 V. Yegnanarayanan, A Parthiban. 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.
Cite this article
V. Yegnanarayanan, A. Parthiban, Chromatic number of graphs with special distance sets-III, J. Math. Comput. Sci. 2 (2012), 1257–1268.
BibTeX
@article{Yegnanarayanan2012,
author = {Yegnanarayanan, V. and Parthiban, A},
title = {Chromatic number of graphs with special distance sets-III},
journal = {J. Math. Comput. Sci.},
volume = {2},
year = {2012},
pages = {1257--1268},
doi = {}
}