International Journal of Combinatorics
Volume 2012 (2012), Article ID 284383, 9 pages
http://dx.doi.org/10.1155/2012/284383
Research Article

Total Vertex Irregularity Strength of the Disjoint Union of Sun Graphs

Slamin,1 Dafik,2 and Wyse Winnona2

1Information System Study Program, University of Jember, Jember 68121, Indonesia
2Mathematics Education Study Program, University of Jember, Jember 68121, Indonesia

Received 11 January 2011; Accepted 31 March 2011

Academic Editor: R. Yuster

Copyright © 2012 Slamin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A vertex irregular total 𝑘 -labeling of a graph 𝐺 with vertex set 𝑉 and edge set 𝐸 is an assignment of positive integer labels { 1 , 2 , … , 𝑘 } to both vertices and edges so that the weights calculated at vertices are distinct. The total vertex irregularity strength of 𝐺 , denoted by t v s ( 𝐺 ) is the minimum value of the largest label 𝑘 over all such irregular assignment. In this paper, we consider the total vertex irregularity strengths of disjoint union of 𝑠 isomorphic sun graphs, t v s ( 𝑠 𝑀 𝑛 ) , disjoint union of 𝑠 consecutive nonisomorphic sun graphs, ⋃ t v s ( 𝑠 𝑖 = 1 𝑀 𝑖 + 2 ) , and disjoint union of any two nonisomorphic sun graphs t v s ( 𝑀 𝑘 ∪ 𝑀 𝑛 ) .