Some new results on equitable tree-coloring parameters of graphs

Abstract

Equitable tree-coloring addresses a structure decomposition problem in communication networks while considering security aspects. Specifically, an equitable tree-t-coloring of a graph is a vertex t-coloring such that each color class induces a forest and the size of any two color classes differs by at most one. This paper demonstrated if G is an equitably tree-t-colorable graph and H is an arbitrary graph with less than 2t vertices ($n<2t$), it is possible to construct an equitable tree-t-coloring of the corona product graph $G\circ H$ in cubic time. Additionally, the equitable tree-coloring of the extended corona product formed by combining graphs G and H has also been investigated.