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