Some Higher Order Triangular Sum Labeling of Graphs

Abstract

A (p,q) graph G is said to admit n th order triangular sum labeling if its vertices can be labeled by non negative integers such that the induced edge labels obtained by the sum of the labels of end vertices are the first q n th order triangular numbers. A graph G which admits n th order triangular sum labeling is called n th order triangular sum graph. In this paper we prove that paths, combs, stars, subdivision of stars, bistars and coconut trees admit fourth, fifth and sixth order triangular sum labelings.