A generalization of Fiedler's lemma and the spectra of H-join of graphs

A new generalization of Fiedler's lemma is obtained by introducing the concept main function a matrix. As applications, universal spectra H-join any graphs (possibly non-regular) and adjacency H-generalized join constrained (arbitrary) vertex subsets are obtained. The generalized corona deduced from graphs. Also, construction infinitely many pairs non-regular cospectral provided.