Edge Irregularity Strength of some Related Graphs to Tp-Tree

Abstract

For a graph G = (V,E), let : V (G) → {1, 2, · · · k} to be vertex k-labeling. An edge irregular k-labeling is defined as follows: for each edge e = xy a weight wt(xy) is given by wt(xy) = (x) + (y) such that wt(xy) = wt(x′y′) for every two different edges xy and x′y′. The edge irregularity strength of G, written by es(G), is the least k for which the graph G has an edge irregular k-labeling. In this paper we find the edge irregularity strength of a Tp-tree (transformed tree) and some related graphs to Tp-trees.

Key words and phrases. Edge irregularity strength, Tp-tree.

2010 Mathematics Subject Classification. 05C78