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Computing the Edge Irregularity Strength of Bipartite Graphs and Wheel Related Graphs

Ahmad Ali, Asim Muhammad Ahsan, Assiri Basem, Semaničová-Feňovčíková Andrea

Fundamenta Informaticae

2020

Vol. 174, nr 1

1--13

A vertex labeling φ : V(G) → {1, 2,... , k} is called an edge irregular k-labeling of a graph G if all edges in G have unique weights. The weight of an edge is defined as the sum of the labels of its incident vertices. The minimum k for which the graph G has an edge irregular k-labeling is called the edge irregularity strength of G, denoted by es(G). In this paper we perform a computer based experiment dealing with the edge irregularity strength of complete bipartite graphs. We also present some bounds on this parameter for wheel related graphs.