An Analysis upon Total Domination of Colouring and Transversals of Graphs: Exploring various aspects of bounded monochromatic component colorings in graph theory

Abstract

A vertex- coloring of a graph is called a bounded monochromatic component colorings (BMC) if every color-class induces monochromatic components containing at most a certain bounded num¬ber of vertices. A proper coloring for instance is a BMC coloring in which every color-class induces monochromatic components of order one. We investigate three different aspects of BMC colorings.