Unitary Addition Cayley Signed Graphs

Authors

  • Deepa Sinha
  • Ayushi Dhama
  • B.D. Acharya

Abstract

A signed graph (or sigraph in short) is an ordered pair S = (Su,), where Su is a graph G = (V, E) and : E !{+,−} is a function from the edge set E of Su into the set {+,−}. For a positive integer n, the unitary addition Cayley graph Gn is the graph whose vertex set is Zn, the ring of integersmodulo n and if Un denotes set of all units of the ring, then two vertices a and b are adjacent if and only if a + b 2 Un. For a positive integer n, the unitary addition Cayley sigraph n = (un,) is definedas the sigraph, where u n is the unitary addition Cayley graph and for an edge ab of n, phi(ab) =¨+ if a 2 Un or b 2 Un,− otherwise. In this paper, we have obtained a characterization of balanced and clusterable unitary addition Cayley sigraphs. Further, we have established a characterization of canonically consistent unitary additionCayley sigraphs n, where n has at most two distinct odd prime factors.

Downloads

Issue

Section

Mathematical Analysis

How to Cite

Unitary Addition Cayley Signed Graphs. (2013). European Journal of Pure and Applied Mathematics, 6(2), 189-210. https://www.ejpam.com/index.php/ejpam/article/view/1929