Laplacian integral signed graphs with few cycles

Abstract

A connected graph with n vertices and m edges is called k-cyclic graph if k=m−n+1. We call a signed graph is Laplacian integral if all eigenvalues of its Laplacian matrix are integers. In this paper, we will study the Laplacian integral k-cyclic signed graphs with k=0,1,2, 3 and determine all connected Laplacian integral signed trees, unicyclic, bicyclic and tricyclic signed graphs.

Keywords

• signed graph
• laplacian integral graph
• spectrum