Restrained star edge coloring of graphs and its application in optimal & safe storage practices

Authors

DOI:

https://doi.org/10.23755/rm.v48i0.1397

Keywords:

Graph coloring, Path coloring, Star edge coloring, Restrained star edge coloring, Restrained Star Chromatic Index

Abstract

In this paper we introduce the concept of restrained star edge coloring of graphs by restraining the conditions of the star coloring of graphs. The restrained star edge coloring of graphs is a path based graph coloring which is said to be proper if all the bichromatic subgraphs of the graph are in the form of a galaxy. The minimum requirement for this coloring is its restrained star chromatic index, denoted as χ'rs. This paper exclusively explains, the restrained star edge coloring of several families of graphs including path, cycle, wheel, etc., and provides the exact value of its respective restrained star chromatic index, χ'rs with the usage of appropriate illustrations. In addition to this, an application of this coloring in the optimal utilization of storage spaces and in ensuring safe storage practices is also briefly elaborated.

Author Biographies

  • W. Evangeline Lydia, St. John’s College, Palayamkottai, Affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli -627012, Tamilnadu, India
    Research Scholar (Reg.No:22211272092006), PG and Research Department of Mathematics
  • J. Vijaya Xavier Parthipan, St. John’s College, Palayamkottai, Affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli -627012, Tamilnadu, India
    Associate Professor and Head, PG and Research Department of Mathematics

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Published

2023-12-30

Issue

Vol. 48 (2023)

Section

Volume 48-2023

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