On H-irregularity strengths of G-amalgamation of graphs

Faraha Ashraf, Martin Baca, Andrea Semanicova-Fenovcikova, Ayesha Shabbir

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) U E(G) \to {1, 2, ..., k} if for every two different subgraphs H' and H'' isomorphic to H there is $wt_{f}(H') \neq wt_{f}(H'')$, where $wt_{f}(H)= \sum \limits_{v\in V(H)} f(v) + \sum \limits_{e \in E(H)} f(e)$ 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.

Keywords

total (vertex, edge) H-irregular labeling, total (vertex, edge) $H$-irregularity strength, amalgamation of graphs