Spectra of bowtie product of graphs

Abstract

In this paper, we introduce a new graph product, namely, bowtie product. We determine the generalized characteristic polynomial of the bowtie product of graphs and consequently, we obtain the characteristic polynomial of the adjacency martix, the Laplacian matrix, the signless Laplacian matrix and the normalized Laplacian matrix of this graph. Also, from these results, we obtain the [Formula: see text]-spectra of some families of bowtie product of graphs. As an application, we obtain infinite pairs of [Formula: see text]-cospectral graphs and construct infinite number of [Formula: see text]-integral graphs.