RT Journal Article
SR Electronic
A1 Bača, Martin
A1 Ryan, Joe
A1 Semaničová-Feňovčíková, Andrea
T1 On the Total Edge Irregularity Strength of Disjoint Union of Graphs
JF Acta Mechanica Slovaca
YR 2015
VO 19
IS 1
SP 60
OP 65
DO 10.21496/ams.2015.008
UL https://www.actamechanica.sk/artkey/ams-201501-0008.php
AB For a simple graph G=(V(G),E(G)), a total labeling f: V(G)υE(G) → {1,2,...,k} is called k-labeling. The weight of an edge xy in G, denoted by wtf(xy), is the sum of the edge label itself and the labels of end vertices x and y, i.e. wtf(xy)=f(x)+f(xy)+f(y). A total k-labeling is defined to be an edge irregular total k-labeling of the graph G if for every two different edges xy and x'y' there is wtf(xy)≠wtf(x'y'). The minimum k for which the graph G has an edge irregular total k-labeling is called the total edge irregularity strength of G, denoted by tes(G). In this paper, we estimate the upper bound of the total edge irregularity strength of disjoint union of multiple copies of a graph and we prove that this upper bound is tight.