### 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.

**How to Cite this Article:**V. Yegnanarayanan, A Parthiban, Chromatic number of graphs with special distance sets-III, J. Math. Comput. Sci., 2 (2012), 1257-1268 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.

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