COMPUTATION OF b-CHROMATIC TOPOLOGICAL INDICES OF SOME GRAPHS AND ITS DERIVED GRAPHS

Abstract

The two fastest-growing subfields of graph theory are graph coloring
and topological indices. Graph coloring is assigning the colors/values to the
edges/vertices or both. A proper coloring of the graph G is assigning colors/values
to the vertices/edges or both so that no two adjacent vertices/edges share the same
color/value. Recently, studies involving Chromatic Topological indices that dealt
with different graph coloring were studied. In such studies, the vertex degrees get
replaced with the colors, and the computation is carried out based on the topological
index of our choice. We focus on b-Chromatic Zagreb indices and b-Chromatic
irregularity indices in this work. This paper discusses the b-Chromatic Zagreb indices
and b-Chromatic irregularity indices of the gear graph, star graph, and its
derived graphs such as the line and middle graph.