On distance signless Laplacian spectrum of graphs and spectrum of zero divisor graphs of ℤ<sub>n</sub>
S. Pirzada, Bilal Ahmad Rather, M. Aijaz, T. A. Chishti
Abstract
For a simple connected graph G of order n, we obtain the distance signless Laplacian spectrum of the joined union of regular graphs G1,G2,…,Gn 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 Zn for some values of n. We show that Γ(Zn) is not in general distance signless Laplacian integral for n=pz, where p is any prime and z≥ 2. Also, we find the spectrum of Γ(Zpz) for certain values of z.
Topics & Concepts
MathematicsCombinatoricsSpectrum (functional analysis)Adjacency matrixSimple graphLaplacian matrixDiscrete mathematicsGraphPhysicsQuantum mechanicsGraph theory and applicationsFinite Group Theory ResearchRings, Modules, and Algebras