Strongly multiplicative labeling of certain tree derived networks

Abstract

A graph $G=(V(G), E(G))$ with $p$ vertices is said to be strongly multiplicative if the vertices of $G$ can be labeled with $p$ distinct integers $1,2, \ldots, p$ such that the labels induced on the edges by the product of labels of the end vertices are all distinct [3]. In this paper we prove that the $X$ - tree, Hypertree and shuffle Hypertree are strongly multiplicative for all $n \geq 2$.