On H-irregularity strengths of G-amalgamation of graphs
| Main Authors: | Ashraf, Faraha; Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan, Baca, Martin; Department of Applied Mathematics and Informatics, Technical University, Kosice, Slovak Republic, Semanicova-Fenovcikova, Andrea; Department of Applied Mathematics and Informatics, Technical University, Kosice, Slovak Republic, Shabbir, Ayesha; Government College University Faisalabad, Sahiwal Campus, Pakpatan Road, Sahiwal, Pakistan |
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| Other Authors: | Slovak Science and Technology Assistance Agency under the contract No. APVV-15-0116 |
| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB
, 2017
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| Subjects: | |
| Online Access: |
http://www.ejgta.org/index.php/ejgta/article/view/391 http://www.ejgta.org/index.php/ejgta/article/view/391/pdf_58 |
Daftar Isi:
- 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.