Mod difference labeling of some classes of digraphs
Authors :
B Sooryanarayana 1 * and Sunita Priya D Silva 2
Author Address :
1 Department of Mathematics, Dr. Ambedkar Institute of Technology, Bangalore-560056, India.
2 Department of Mathematics, Sahyadri College of Engineering and Management, Mangalore-575009, India.
*Corresponding author.
Abstract :
A graph is a \textit{difference graph} if there is a bijection $f$ from $ V$ to a set of positive integers $S$ such that $ xy \in E $ if and only if $|f(x)-f(y)|\in S$. A digraph $D=(V,E)$ is a \textit{mod difference digraph } if there exist a positive integer $ m$ and labeling $ L : V \rightarrow \{1, 2, . . .,m - 1\}$ such that $(x, y) \in E $ if and only if $L(y) - L(x) \equiv L(w)(mod \ m)$ 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.
DOI :
Article Info :
Received : July 17, 2019; Accepted : December 12, 2019.
