Net Laplacian spectrum of some products built on the simple corona of a signed graph

Abstract

For a signed graph Σ, if A(Σ) and D±(Σ) are its adjacency matrix and diagonal matrix of net degrees, then the net Laplacian matrix of Σ is N(Σ) = D±(Σ) − A(Σ). A simple corona Σ ◦K1 is obtained by attaching a positive pendant edge at every vertex of Σ. In this paper, we define the three products of signed graphs Σ1 and Σ2 based on the simple corona Σ1 ◦ K1, and compute their net Laplacian spectrum when Σ1 is net-regular. As an application, we consider the controllability of the corresponding products..