On distance signless Laplacian spectrum of graphs and spectrum of zero divisor graphs of ℤn. Issue 17 (22nd November 2022)

• Record Type: Journal Article
• Authors: Pirzada, S.; Rather, Bilal A.; Aijaz, M.; Chishti, T. A.
• Is Part Of: Linear & multilinear algebra. Volume 70:Issue 17(2022)
• Page Start: 3354
• Page End: 3369
• Publication Date: 2022-11-22
• Subjects: Distance matrix -- distance signless Laplacian matrix -- zero divisor graphs; 05C50 -- 05C12 -- 15A18; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2020.1838425
• Languages: English
• ISSNs: 0308-1087

Abstract

ABSTRACT: For a simple connected graph G of order n, we obtain the distance signless Laplacian spectrum of the joined union of regular graphs G 1, G 2, …, G n in terms of their adjacency spectrum and the spectrum of an auxiliary matrix. As a consequence, we obtain the distance signless Laplacian spectrum of the zero divisor graphs of finite commutative rings Z n for some values of n . We show that Γ ( Z n ) is not in general distance signless Laplacian integral for n = p z, where p is any prime and z ≥ 2. Also, we find the spectrum of Γ ( Z p z ) for certain values of z .