Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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L(4, 3, 2, 1)-PATH COLORING OF CERTAIN CLASSES OF GRAPHS

  • DHANYASHREE (Department of Mathematics, Amrita School of Engineering) ;
  • K.N. MEERA (Department of Mathematics, Amrita School of Engineering)
  • Received : 2021.10.06
  • Accepted : 2022.04.18
  • Published : 2023.05.30
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Abstract

An L(p1, p2, p3, . . . , pm)-labeling of a graph G is an assignment of non-negative integers, called as labels, to the vertices such that the vertices at distance i should have at least pi as their label difference. If p1 = 4, p2 = 3, p3 = 2, p4 = 1, then it is called a L(4, 3, 2, 1)-labeling which is widely studied in the literature. A L(4, 3, 2, 1)-path coloring of graphs, is a labeling g : V (G) → Z+ such that there exists at least one path P between every pair of vertices in which the labeling restricted to this path is a L(4, 3, 2, 1)-labeling. This concept was defined and results for some simple graphs were obtained by the same authors in an earlier article. In this article, we study the concept of L(4, 3, 2, 1)-path coloring for complete bipartite graphs, 2-edge connected split graph, Cartesian product and join of two graphs and prove an existence theorem for the same.

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Acknowledgement

The authors would like to Thank the Management of Amrita School of Engineering, Bengaluru, Amrita Vishwa Vidyapeetham for all the support and encouragement provided.

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