Connected signed graphs L-cospectral to signed ∞-graphs. Issue 12 (2nd December 2019)

• Record Type: Journal Article
• Authors: Belardo, Francesco; Brunetti, Maurizio
• Is Part Of: Linear & multilinear algebra. Volume 67:Issue 12(2019)
• Page Start: 2410
• Page End: 2426
• Publication Date: 2019-12-02
• Subjects: Signed graph -- Laplacian -- ∞-graph -- spectral determination -- bicyclic; 05C50 -- 05C22; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2018.1494122
• Languages: English
• ISSNs: 0308-1087

Abstract

ABSTRACT: A signed graph is a pair Γ = ( G, σ ), where G = ( V ( G ), E ( G ) ) is a graph and σ : E ( G ) → { + 1, − 1 } is the sign function on the edges of G . For a signed graph we consider the Laplacian matrix defined as L ( Γ ) = D ( G ) − A ( Γ ), where D ( G ) is the matrix of vertex degrees of G and the (signed) adjacency matrix A ( Γ ) . A signed ∞-graph consists of two signed cycles with just one vertex in common. In this paper, we study the Laplacian spectral determination problem for the class of signed ∞-graphs, and we identify all connected L -cospectral mates.