Uniquely List Colorability of Complete Split Graphs

The join of null graph Om and complete graph Kn, denoted by S(m; n), is called a complete split graph. In this paper, we characterize unique list colorability of the graph G = S(m; n). We shall prove that G is uniquely 3-list colorable graph if and only if m>=4, n>=4 and m + n>=10, m(G)>=4 for every 1<=m<=5 and n>=6.The join of null graph Om and complete graph Kn, denoted by S(m; n), is called a complete split graph. In this paper, we characterize unique list colorability of the graph G = S(m; n). We shall prove that G is uniquely 3-list colorable graph if and only if m>=4, n>=4 and m + n>=10, m(G)>=4 for every 1<=m<=5 and n>=6