Achromatic Numbers of $n$-Complete Starfish and $SF(n, 1)$ Graphs

Abstract

The achromatic number of a graph is the largest number of colors that can be assigned to each vertex of the graph such that adjacent vertices are assigned different colors and any two different colors are assigned to some pair of adjacent vertices. In this paper, we find exact values of the achromatic numbers of $n$-complete starfish graphs, and bounds on the achromatic numbers of $SF(n, 1)$ graphs when $n$ is a natural number and $n\geq 3$.