Complete split graph determined by its (signless) Laplacian spectrum.

A complete split graph C S ( n , α ) , is a graph on n vertices consisting of a clique on n − α vertices and an independent set on the remaining α ( 1 ≤ α ≤ n − 1 ) vertices in which each vertex of the clique is adjacent to each vertex of the independent set. In this paper, we prove that C S ( n , α ) is determined by its Laplacian spectrum when 1 ≤ α ≤ n − 1 , and C S ( n , α ) is also determined by its signless Laplacian spectrum when 1 ≤ α ≤ n − 1 and α ≠ 3 . [ABSTRACT FROM AUTHOR]