On H-irregularity strengths of G-amalgamation of graphs

Abstract

A simple graph G = (V (G),E(G)) admits an H-covering if every edge in E(G) belongs at least to one subgraph of G isomorphic to a given graph H. Then the graph G admitting H- covering admits an H-irregular total k-labeling f: V (G)∪E(G) → (1, 2, . . ., k) if for every two different subgraphs H' and H'' isomorphic to H there is wtf (H') ≠ wtf (H'' P), where is the associated H-weight. The minimum k for which the graph G has an H-irregular total k-labeling is called the total H-irregularity strength of the graph G. In this paper, we obtain the precise value of the total H-irregularity strength of G-amalgamation of graphs.