Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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A NOTE ON VERTEX PAIR SUM k-ZERO RING LABELING

  • ANTONY SANOJ JEROME (Department of Mathematics, University College) ;
  • K.R. SANTHOSH KUMAR (Department of Mathematics, University College) ;
  • T.J. RAJESH KUMAR (Department of Mathematics, T.K.M. College of Engineering)
  • Received : 2023.08.14
  • Accepted : 2023.11.28
  • Published : 2024.03.30
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Abstract

Let G = (V, E) be a graph with p-vertices and q-edges and let R◦ be a finite zero ring of order n. An injective function f : V (G) → {r1, r2, …, rk}, where ri ∈ R◦ is called vertex pair sum k-zero ring labeling, if it is possible to label the vertices x ∈ V with distinct labels from R◦ such that each edge e = uv is labeled with f(e = uv) = [f(u) + f(v)] (mod n) and the edge labels are distinct. A graph admits such labeling is called vertex pair sum k-zero ring graph. The minimum value of positive integer k for a graph G which admits a vertex pair sum k-zero ring labeling is called the vertex pair sum k-zero ring index denoted by 𝜓pz(G). In this paper, we defined the vertex pair sum k-zero ring labeling and applied to some graphs.

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Acknowledgement

The authors are thankful to the referee for the useful suggestions.

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