Some aspects of unitary addition Cayley graph of Eisensteinintegers modulo $\textit{n}$

Document Type : Research Paper

Authors

1 Department of mathematics. Assam Don Bosco University, Tepesia. Assam, India.

2 Department of mathematics, Gauhati University, Guwahati, Assam, India.

10.29252/as.2021.2469

Abstract

The unitary addition Cayley graph $G_n[\omega]$ of Eisenstein integers modulo $n$ has the vertex set $\mathbb{E}_n[\omega]$, the set of Eisenstein integers modulo $n$. Any two vertices $x=a_1+\omega b_1$, $y=a_2+\omega b_2$ of $G_n[\omega]$ are adjacent if and only if $gcd(N(x+y),n)=1$, where $N$ is the norm of any element of $\mathbb{E}_n[\omega]$ given by $N(a+\omega b)=a^2+b^2-ab$. In this paper we obtain some basic graph invariants such as degree of the vertices, number of edges, diameter, girth, clique number and chromatic number of unitary addition Cayley graph of Eisenstein integers modulo $n$. This paper also focuses on determining the independence number of the above mentioned graph.
 

Keywords


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