IJPAM: Volume 99, No. 1 (2015)

TOTAL EDGE IRREGULARITY STRENGTH
OF SERIES PARALLEL GRAPHS

Indra Rajasingh$^1$, S. Teresa Arockiamary$^2$
$^1$School of Advanced Sciences
VIT University
Chennai, 600 127, INDIA
$^{2}$Department of Mathematics
Stella Maris College
Chennai, 600 086, INDIA


Abstract. Given a graph $G(V,E)$ a labeling $\partial :V\cup E\rightarrow \left\{1,2,...,k\right\} $ is called an edge irregular total k-labeling if for every pair of distinct edges uv and xy, $\partial (u)+\partial (uv)+\partial (v)\neq \partial (x)+\partial (xy)+\partial (y).$ 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.

Received: March 25, 2014

AMS Subject Classification: 05C78

Key Words and Phrases: irregular total labeling, interconnection networks, total edge irregularity strength, series parallel graphs, labeling

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DOI: 10.12732/ijpam.v99i1.2 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 99
Issue: 1
Pages: 11 - 21


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