Equitable chromatic number of weak modular product of Some graphs

• Kaliraj, K. ^[1] ; Narmadha Devi, R. ^[1] ; Vernold Vivin, J. ^[2]
  1. [1] University of Madras

     University of Madras

     India

     
  2. [2] University College of Engineering Nagercoil.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 41, Nº. 5, 2022, págs. 1051-1062
• Idioma: inglés
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• Resumen

  • An equitable coloring of a graph G is a proper coloring of the vertices of G such that the number of vertices in any two color clases differ by at most one. The equitable chromatic number χ=(G) of a graph G is the minimum number of colors needed for an equitable coloring of G. In this paper, we obtain the equitable chromatic number of weak modular product of two graphs G and H, denoted by G o H.

    First, we consider the graph G o H, where G is the path graph, and H be any simple graph like the path, the cycle graph, the complete graph. Secondly, we consider G and H as the complete graph and cycle graph respectively. Finally, we consider G as the star graph and H be the complete graph and star graph.