IJPAM: Volume 105, No. 4 (2015)

COLORABILITY OF UNITARY CAYLEY DIGRAPHS
OF CYCLIC GROUPS

C. Promsakon
Department of Mathematics
Faculty of Applied Science
King Mongkut's University of Technology North Bangkok
Bangkok, 10800, THAILAND


Abstract. Let $n$ be a positive integer greater than 1, $\mathbb Z_n$ the integer modulo $n$ and $A$ the subset of $\mathbb Z_n$. The Cayley digraph of $\mathbb Z_n$ with a connecting set $A$ , denoted by $Cay(\mathbb Z_n,A)$ is a digraph whose vertex set is $\mathbb Z_n$ and a vertices $x$ and $y$ are adjacent if and only if $y=x+a$ where $a\in A$. We call a Cayley digraph as unitary Cayley digraph if its connecting set is the set of all units in $\mathbb Z_n$.

In this paper, we focus on coloring properties of unitary Cayley digraphs of $\mathbb Z_n$. We show their chromatic numbers and their edge chromatic number.

Received: June 19, 2015

AMS Subject Classification: 46MO5, 05C40, 05C76

Key Words and Phrases: Cayley graphs, coloring, chromatic number, edge-chromatic number, units

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DOI: 10.12732/ijpam.v105i4.5 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 105
Issue: 4
Pages: 639 - 645


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