Edge Irregularity Strength of Graphs: Theoretical Results and Applications to Communication Networks

This paper presents new results on the edge irregularity strength of various graph classes. The exact values are determined for the series composition of the isomorphic uniform theta graphs, expressed as θ (n;m;r) , in particular for the cases where $$n = m = 3$$ and $$n = 4, m = 3$$ with r ≥ 2 . Additionally, the edge irregularity strength is obtained for the shadow graph of paths with odd length; and the square of the path P₆ and the theta graph θ (1,4,4) , each extended by adding a single pendant edge. Furthermore, the paper explores an application of edge irregularity strength in optimizing path selection within communication networks.