Zoran Stanic: On the spectrum of the net Laplacian matrix of a signed graph, 205-213

Abstract:

Given a signed graph $\dot{G}$, let $A_{\dot{G}}$ and $\smash{D^{\pm}_{\dot{G}}}$ be its standard adjacency matrix and the diagonal matrix of vertex net-degrees, respectively. The net Laplacian matrix of $\dot{G}$ is defined to be $\smash{N_{\dot{G}}=D^{\pm}_{\dot{G}}-A_{\dot{G}}}$. In this paper we give some spectral properties of $N_{\dot{G}}$. We also point out some advantages and some disadvantages of using the net Laplacian matrix instead of the standard Laplacian matrix in study of signed graphs.

Key Words: (Net) Laplacian matrix, largest eigenvalue, join, graph product.

2010 Mathematics Subject Classification: Primary 05C50; Secondary 05C22.