Colorings of the Graph K ᵐ 2 + Kn

Abstract

In this paper, we characterize chromatically unique, determine list-chromatic number and characterize uniquely list colorability of the graph G = Km 2 + Kn. We shall prove that G is χ-unique, ch(G) = m + n, G is uniquely 3-list colorable graph if and only if 2m + n > 7 and m > 2