Mod difference labeling of some classes of digraphs

B Sooryanarayana; Sunita Priya D Silva

doi:10.26637/MJM0801/0006

Abstract

A graph is a difference graph if there is a bijection $f$ from $V$ to a set of positive integers $S$ such that $x y \in E$ if and only if $|f(x)-f(y)| \in S$. A digraph $D=(V, E)$ is a mod difference digraph if there exist a positive integer $m$ and labeling $L: V \rightarrow\{1,2, \ldots, m-1\}$ such that $(x, y) \in E$ if and only if $L(y)-L(x) \equiv L(w)(\bmod m)$ for some $w \in V$. In this paper, we prove that the complete bipartite digraphs, oriented binary trees, ladder graphs and fan graphs are mod difference digraphs.

Keywords:

Difference labeling, mod difference labeling, digraphs.

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

B Sooryanarayana Department of Mathematics, Dr. Ambedkar Institute of Technology, Bangalore-560056, India
Sunita Priya D Silva Department of Mathematics, Sahyadri College of Engineering and Management, Mangalore-575009, India.

Pages: 32-36
Date Published: 01-01-2020
Vol. 8 No. 01 (2020): Malaya Journal of Matematik (MJM)

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