On H-irregularity strengths of G-amalgamation of graphs - Faraha Ashraf; Martin Baca; Andrea Semanicova-Fenovcikova; Ayesha Shabbir (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2017)
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) → 1, 2, ..., k if for every two different subgraphs H' and H'' isomorphic to H there is wt_f(H') ≠ wt_f(H''), where wt_f(H)= _vV(H) f(v) + _e 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.