Spectra of F-sum and F-product of graphs

Several graph operations based on subdivision graph and its variants have been introduced by many researchers and their spectral properties have been studied. The F-sum and F-product of graphs are one among these graph operations. In literature, many topological indices of F-sum and F-product of graphs have been examined. In this paper, we first introduce two matrix forms named as F-sum matrix and F-product matrix and describe their spectra, and then using the spectra of these matrices, we compute the spectra of F-sum and F-product of graphs.