Abstract: The subdivision Q-neighborhood vertex corona G1□·_QG2 of two regular graphs G₁ and G₂ for regular is the graph obtained from vertex disjoint union of Q(G1) and |V(G1)| copies of G₂, and by joining the neighbors of the i^th vertex of |V(G1)| to every vertex in the i^th copy of G₂; the subdivision Q-neighborhood edge corona G1□— _QG2 is the graph obtained from vertex disjoint union of Q(G1) and |I(G1)| copies of G₂, and by joining the neighbors of the i^th vertex of I(G1) to every vertex in the i^th copy of G₂, where Q(G1) is obtained from G₁ by inserting a new vertex into every edge of G₁ and then joining by edges those pair of new vertices which lie on adjacent edges of G₁, and I(G1) is denoted by the set of such new vertices inserted in each edge of G₁. Based on above, the generalized characteristic polynomial and Φ-spectrum of G1□·_QG2 and G1□— _QG2 are determined, respectively. As an application, their normalized Laplacian spectrum are obtained. Besides, infinitely many pairs of Φ-cospectral mates are also constructed.

Key words: subdivision Q-neighborhood vertex corona, subdivision Q-neighborhood edge corona, generalized characteristic polynomial, Φ-cospectral graphs