A(alpha) matrix of commuting graphs of non-abelian groups

For a finite group G and a subset X not equal empty set of G, the commuting graph, indicated by G = C(G, X), is the simple connected graph with vertex set X and two distinct vertices x and y are edge connected in G if and only if they commute in X. The A(alpha) matrix of G is specified as A(alpha) (G) = alpha D(G) + (1-alpha)A(G), alpha is an element of [0, 1], where D(G) is the diagonal matrix of vertex degrees while A (G) is the adjacency matrix of G. In this article, we investigate the A(alpha) matrix for commuting graphs of finite groups and we also find the A(alpha) eigenvalues of the dihedral, the semidihedral and the dicyclic groups. We determine the upper bounds for the largest A a eigenvalue for these graphs. Consequently, we get the adjacency eigenvalues, the Laplacian eigenvalues, and the signless Laplacian eigenvalues of these graphs for particular values of alpha. Further, we show that these graphs are Laplacian integral.