The reflexive vertex strength on cycle and generalized friendship graph

Ika Hesti Agustin, M. Imam Utoyo, Dafik, N. Mohanapriya, Slamin

Research output: Contribution to journalArticlepeer-review


Let G be a simple, un-directed and connected graph. The graph G has a pair of sets (V (G),E(G)), where V (G) is nonempty vertex set and E(G) is an unordered pair of sets with two distinct vertices u,v in V (G). A total k-labeling is defined as a function fe from the edge set to a set {1, 2, 3,...,ke} and a function fv from the vertex set to a set {0, 2, 4,..., 2kv}, where k =max{ke, 2kv}. The total k-labeling is a vertex irregular reflexivek-labeling of the graph G, if for every two different vertices u and u′ of G, wt(u) wt(u′), where wt(u) = fv(u) + uv E(G)fe(uv). The reflexive vertex strength of the graph G, denoted by rvs(G) is the minimum k for graph G which has a vertex irregular reflexive k-labeling. In this paper, we determined the exact value of the reflexive vertex strength of cycle and generalized friendship graph.

Original languageEnglish
Article number2350137
JournalAsian-European Journal of Mathematics
Issue number8
Publication statusPublished - 1 Aug 2023


  • Reflexive vertex strength
  • cycle graph
  • generalized friendship graph
  • vertex irregular reflexive labeling


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