Chromatic Number of Graphs with Special Distance Sets-V ()

Venkataraman Yegnanarayanan, Angamuthu Parthiban

Department of Mathematics, Velammal Engineering College, Chennai, India.

**DOI: **10.4236/ojdm.2013.31001
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Department of Mathematics, Velammal Engineering College, Chennai, India.

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 *x*(*G*(*Z*,*D*) )=4 where *P* is a set of Prime numbers. So we can allocate the subsets *D* of *P* to four classes, accordingly as is 1 or 2 or 3 or 4. In this paper we have considered the open problem of characterizing class three and class four sets when the distance set *D *is not only a subset of primes *P* but also a special class of primes like Additive primes, Deletable primes, Wedderburn-Etherington Number primes, Euclid-Mullin sequence primes, Motzkin primes, Catalan primes, Schroder primes, Non-generous primes, Pell primes, Primeval primes, Primes of Binary Quadratic Form, Smarandache-Wellin primes, and Highly Cototient number primes. We also have indicated the membership of a number of special classes of prime numbers in class 2 category.

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V. Yegnanarayanan and A. Parthiban, "Chromatic Number of Graphs with Special Distance Sets-V," *Open Journal of Discrete Mathematics*, Vol. 3 No. 1, 2013, pp. 1-6. doi: 10.4236/ojdm.2013.31001.

Conflicts of Interest

The authors declare no conflicts of interest.

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