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On the Construction of the Reflexive Vertex - Labeling of Any Graph with Pendant Vertex

Author

Listed:
  • I. H. Agustin
  • M. I. Utoyo
  • Dafik
  • M. Venkatachalam
  • Surahmat

Abstract

A total - labeling is a function from the edge set to first natural number and a function from the vertex set to non negative even number up to , where . A vertex irregular reflexive -labeling of a simple, undirected, and finite graph is total - labeling, if for every two different vertices and of , , where . The minimum for graph which has a vertex irregular reflexive - labeling is called the reflexive vertex strength of the graph , denoted by . In this paper, we determined the exact value of the reflexive vertex strength of any graph with pendant vertex which is useful to analyse the reflexive vertex strength on sunlet graph, helm graph, subdivided star graph, and broom graph.

Suggested Citation

  • I. H. Agustin & M. I. Utoyo & Dafik & M. Venkatachalam & Surahmat, 2020. "On the Construction of the Reflexive Vertex - Labeling of Any Graph with Pendant Vertex," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2020, pages 1-8, October.
    • Handle: RePEc:hin:jijmms:7812812
    DOI: 10.1155/2020/7812812
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