Adjacent Vertex Reducible Edge Coloring of Selected Graph Classes

Abstract

If there is a function f : E(G) → {1, 2, 3, . . . , K} suchthat for any two adjacent vertices u and v of the samedegree, the sets S(u) and S(v) are equal, where S(u) ={f(uv), uv ∈ E(G)}, then a graph G = (V, E) is said tohave an adjacent vertex reducible edge coloring. The term“chromatic number of adjacent vertex reducible edge coloring” refers to the highest value of K. The purpose of this study is to ascertain the chromatic number for adjacent vertex reducible edge coloring of specific graphs, including mirror graphs, alternate triangular cycles, prism wheel graphs, double wheel graphs, antiprism graphs, crown (or sun) graphs, degree splitting graphs, and H-graph.