Product irregularity strength of graphs

Abstract

a b s t r a c tConsider a simple graph G with no isolated edges and at most one isolated vertex. AThe goal is to obtain a product-irregular labeling that minimizes the maximum label. This minimum value is called the product irregularity strength. The analogous concept of irregularity strength, with sums in place of products, has been introduced by Chartrand et al. and investigated by many authors.

Product irregularity strength of certain graphs

“…The concept was introduced by M. Anholcer in [4]. 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.…”

A new upper bound for the total vertex irregularity strength of graphs

“…The two last results hold also for paths P n and all the Hamiltonian graphs of order n. In the same paper upper bounds for grids and toroidal grids were given. Theorem 1.10 ( [3]) For every ε > 0 there exist n (0) j ,j = 1, . .…”

Product irregularity strength of graphs with small clique cover number

“…This concept was first introduced by Anholcer in [1] as a multiplicative version of the well-studied concept of irregularity strength of graphs introduced by Chartrand et al in [4] and studied later quite extensively (see for example [3,7,8,11]). A concept similar to product-irregular labelling is the product anti-magic labeling of a graph, where it is required that the labeling ω is bijective (see [9,12]).…”

“…In [1] Anholcer gave upper and lower bounds on product irregularity strength of graphs. The main results in [1] are estimates for product irregularity strength of cycles, in particular it was proved that for every n > 2…”