TOTAL EDGE IRREGULARITY STRENGTH OF SERIES PARALLEL GRAPHS

I Rajasingh,S.T Arockiamary

doi:10.12732/ijpam.v99i1.2

Abstract

Given a graph G(V,E) a labeling @ : V ∪E → {1,2,...,k} is called an edge irregular total k-labeling if for every pair of distinct edges uv and xy, @(u)+@(uv)+@(v) 6 @(x)+@(xy)+@(y). The minimum k for which G has an edge irregular total k-labeling is called the total edge irregularity strength. In this paper we consider series composition of uniform theta graphs and obtain its total edge irregularity strength. We have determined the exact value of the total edge irregularity strength of this graph. We have further given an algorithm to prove the result.

Highlights

A basic feature for a system is that its components are connected together by Received: March 25, 2014 §Correspondence author c 2015 Academic Publications, Ltd. url: www.acadpubl.euI
It is undoubted that the power of a system is highly dependent upon the connection pattern of components in the system
Interconnection networks are becoming increasingly pervasive in many different applications with the operational costs and characteristics of these networks depending considerably on the application

Summary

Introduction

A basic feature for a system is that its components are connected together by Received: March 25, 2014 §Correspondence author c 2015 Academic Publications, Ltd. url: www.acadpubl.euI. AMS Subject Classification: 05C78 Key Words: irregular total labeling, interconnection networks, total edge irregularity strength, series parallel graphs, labeling The total edge (vertex ) irregular strength of G is denoted by tes(G) (tvs(G)).

Results

Conclusion