On inclusive distance vertex irregular labelings
| Main Authors: | Baca, Martin; Department of Applied Mathematics and Informatics, Technical University, Letna 9, Kosice, Slovakia, Semanicova-Fenovcikova, Andrea; Department of Applied Mathematics and Informatics, Technical University, Letna 9, Kosice, Slovakia, Slamin, S.; Information System Study Program, University of Jember, Jl. Kalimantan 37 Jember, Indonesia, Sugeng, Kiki A.; Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Indonesia, Kampus UI Depok, Depok 16424, Indonesia |
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| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB
, 2018
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| Subjects: | |
| Online Access: |
https://www.ejgta.org/index.php/ejgta/article/view/463 https://www.ejgta.org/index.php/ejgta/article/view/463/pdf_65 |
Daftar Isi:
- For a simple graph G, a vertex labeling f : V(G) → {1, 2, ..., k} is called a k-labeling. The weight of a vertex v, denoted by wtf(v) is the sum of all vertex labels of vertices in the closed neighborhood of the vertex v. A vertex k-labeling is defined to be an inclusive distance vertex irregular distance k-labeling of G if for every two different vertices u and v there is wtf(u) ≠ wtf(v). The minimum k for which the graph G has a vertex irregular distance k-labeling is called the inclusive distance vertex irregularity strength of G. In this paper we establish a lower bound of the inclusive distance vertex irregularity strength for any graph and determine the exact value of this parameter for several families of graphs.