Distance-2 Chromatic Number of the Central and Shadow Graphs of a Cycle and its Application to Computer Science

Authors

  • Merliza Libao Mathematics Department, Caraga State University, Butuan City, Philippines
  • Kyla B. Abarca Mathematics Department, Caraga State University, Butuan City, Philippines

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i2.5734

Keywords:

Distance-2 Chromatic Number, Graph Coloring, Shadow Graphs, Central Graphs, Cycle Graphs, Graph Theory, Computer Science Applications, Resource Allocation

Abstract

Let \(G=(V(G),E(G))\) be a graph. The chromatic number of a graph \(G\), \(\chi(G)\), is the minimum number of colors needed to color the vertices such that no two adjacent vertices share the same color. The distance-2 chromatic number of G, \(\chi_2 (G)\), extends this by ensuring that no two vertices within distance 2 share the same color in G. This study investigates \(\chi_2 (G)\) for the Shadow and Central graphs of cycles. While previous research has focused on certain graphs, we expand the analysis to the Shadow and Central graphs of cycles, with potential applications in computer science, particularly in network topology and resource allocation.

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Published

2025-05-01

Issue

Vol. 18 No. 2: (April 2025)

Section

Discrete Mathematics

License

Copyright (c) 2025 Merliza Libao, Kyla B. Abarca

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How to Cite

Distance-2 Chromatic Number of the Central and Shadow Graphs of a Cycle and its Application to Computer Science. (2025). European Journal of Pure and Applied Mathematics, 18(2), 5734. https://doi.org/10.29020/nybg.ejpam.v18i2.5734