Spectral radii of friendship graphs and their connected induced subgraphs. Issue 1 (2nd January 2023)

• Record Type: Journal Article
• Authors: Seeger, Alberto; Sossa, David
• Is Part Of: Linear & multilinear algebra. Volume 71:Issue 1(2023)
• Page Start: 63
• Page End: 87
• Publication Date: 2023-01-02
• Subjects: Friendship graphs -- spectral radius -- cospectrality -- complementarity eigenvalue -- spectral redundancy -- separability index; 05C50 -- 15A42; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2021.2017836
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract : The purpose of this work is to shed some new light on the spectral properties of the family of friendship graphs and, more generally, the family of weak-friendship graphs. A weak-friendship graph is a connected induced subgraph of a friendship graph. We characterize the spectral radius of a friendship graph and of each one of its connected induced subgraphs. We prove that the separability index of the family of weak-friendship graphs is equal to 2. We provide exact and asymptotic estimates for the number of complementarity eigenvalues of a weak-friendship graph.