A New Upper Bound for the Irregularity Strength of Graphs

Abstract

A weighting of the edges of a graph is called irregular if the weighted degrees of the vertices are all different. In this note we show that such a weighting is possible from the weight set {1, 2, . . . , 6 n δ } for all graphs not containing a component with exactly 2 vertices or two isolated vertices.

Product irregularity strength of certain graphs

“…As we can see, it is the multiplicative version of the well known irregularity strength introduced by Chartrand et al in [5] and studied by numerous authors (the best result for general graphs can be found in Kalkowski, Karoński and Pfender [6], while e.g. trees and forests have been studied e.g.…”

Note on the group edge irregularity strength of graphs

“…The smallest value of s that allows an irregular labeling is called the irregularity strength of G and denoted by s(G). This problem was one of the major sources of inspiration in graph theory [3,4,5,6,7,12,18,19,20,23,26,28]. For example the concept of G-irregular labeling is a generalization of irregular labeling on Abelian groups.…”

On H-irregularity strengths of G-amalgamation of graphs

“…Namely, the authors in [17] have proved that s(G) ≤ 6 n/δ < 6n/δ + 6. Currently Majerski and Przybyło [19] proved that s(G) ≤ (4 + o(1))n/δ + 4 for graphs with minimum degree δ ≥ √ n ln n. For a given vertex labeling h : V (G) → {1, 2, .…”