The vertex irregular reflexive labeling of some almost regular graph

Ika Hesti Agustin, M. Imam Utoyo, Dafik, M. Venkatachalam

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

A labeling of a graph is a mapping of graphs (vertices or edges) into a set of positive integers or a set of non-negative integers. Let H be a connected, simple, nontrivial, and un-directed graph with the vertex set V (H) and the edge set E(H). A total k-labeling is a function fe from E(H) to first natural number ke and a function fv from V (H) to non negative even number up to 2kv, where k = maxfke; 2kvg. A vertex irregular reflexive k-labeling of the graph G is total k-labeling, if for every two different vertices have different weight, where the weight of a vertex is the sum of labels of edges which are incident this vertex and the vertex label itself. The reflexive vertex strength of the graph G, denoted by rvs(G) is a minimum k such that graph G has a vertex irregular reflexive k-labelling. In this paper, We will determine the exact value of reflexive vertex strength on ladder graph and bipartite complete (K2;n).

Original languageEnglish
Pages (from-to)83-91
Number of pages9
JournalPalestine Journal of Mathematics
Volume10
Issue numberSpecial Issue II
Publication statusPublished - 2021

Keywords

  • Bipartite complete (K2
  • Ladder graph
  • N)
  • Reflexive vertex strength
  • Vertex irregular reflexive k-labelling

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