A Study on the Modular Sumset Labeling of Graphs

Abstract: For a positive integer $n$, let $\mZ$ be the set of all non-negative integers modulo $n$ and $\sP(\mZ)$ be its power set. A modular sumset valuation or a modular sumset labeling of a given graph $G$ is an injective function $f:V(G) \to \sP(\mZ)$ such that the induced function $f^+:E(G) \to \sP(\mZ)$ defined by $f^+ (uv) = f(u)+ f(v)$. A sumset indexer of a graph $G$ is an injective sumset valued function $f:V(G) \to \sP(\mZ)$ such that the induced function $f^+:E(G) \to \sP(\mZ)$ is also injective. In this paper, some properties and characteristics of this type of modular sumset labeling of graphs are being studied.