• SECOND AND THIRD ORDER TRIANGULAR SUM LABELING OF GRAPHS

Abstract

A (p, q) graph G is said to admit a second (or third) order triangular sum labeling if its vertices can be labeled by nonnegative integers such that induced edge labels obtained by the sum of the labels of end vertices are the first second (or third) order triangular numbers . A graph G which admits a second (or third) order triangular sum labeling is called a second (or third) order triangular sum graph. In this paper we prove that paths, stars, coconut trees, bistars and Bm,n,k admit second and third order triangular sum labeling.