Signed graphs with integral net Laplacian spectrum

Abstract

Given a signed graph G˙, let AG˙ and DG˙± be its standard adjacency matrix and the diagonal matrix of net-degrees, respectively. The net Laplacian matrix of G˙ is defined as NG˙=DG˙±−AG˙. In this paper we investigate signed graphs whose net Laplacian spectrum consists entirely of integers. The focus is mainly on the two extreme cases, the one in which all eigenvalues of NG˙ are simple and the other in which NG˙ has 2 or 3 (distinct) eigenvalues. Both cases include structure theorems, degree constraints and particular constructions of new examples. Several applications in the framework of control theory are reported.

Locations

• AKCE International Journal of Graphs and Combinatorics - View - PDF