Which multicone graphs are determined by their signless Laplacian spectrum? (The proof of a conjecture). (2nd January 2019)

• Record Type: Journal Article
• Authors: Abdian, Ali Zeydi; Pouyandeh, Sara; Askari, Bahman
• Is Part Of: Journal of discrete mathematical sciences & cryptography. Volume 22:Number 1(2019)
• Page Start: 91
• Page End: 99
• Publication Date: 2019-01-02
• Subjects: (2010) 05C50 -- 20D30; DS graph -- Multicone graph -- Signless Laplacian spectrum; Computer science -- Mathematics -- Periodicals; Cryptography -- Periodicals; Computer science -- Mathematics; Cryptography; Periodicals; 004.0151
• DOI: 10.1080/09720529.2019.1578082
• Languages: English
• ISSNs: 0972-0529

Abstract

Abstract: A multicone graph is defined to be the join of a clique and a regular graph. Let Km and denote a complete graph on m vertices and the complement of a complete graph on n vertices, respectively. In [X. Liu and P. Lu, Signless Laplacian spectral characterization of some joins, Electron. J. Linear Algebra 30.1 (2015)], it have been conjectured that the multicone graphs are determined by their signless Laplacian spectrum. In this short note, we prove this conjecture for n ≠ 3.