scholarly journals Seidel Laplacian and Seidel Signless Laplacian Spectrum of the Zero-divisor Graph on the Ring of Integers Modulo

2021 ◽  
Vol 9 (6) ◽  
pp. 917-926
Author(s):  
Magi P M ◽  
Sr.Magie Jose ◽  
Anjaly Kishore
Keyword(s):  
Zero Divisor ◽  
Laplacian Spectrum ◽  
Ring Of Integers ◽  
Signless Laplacian Spectrum ◽  
Zero Divisor Graph ◽  
Signless Laplacian

scholarly journals On Laplacian Eigenvalues of the Zero-Divisor Graph Associated to the Ring of Integers Modulo n

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 482
Author(s):  
Bilal A. Rather ◽  
Shariefuddin Pirzada ◽  
Tariq A. Naikoo ◽  
Yilun Shang
Keyword(s):  
Commutative Ring ◽  
Zero Divisor ◽  
Simple Graph ◽  
Laplacian Spectrum ◽  
Laplacian Eigenvalues ◽  
Ring Of Integers ◽  
Zero Divisor Graph ◽  
Zero Divisors ◽  
Vertex Set ◽  
Positive Integers

Given a commutative ring R with identity 1≠0, let the set Z(R) denote the set of zero-divisors and let Z*(R)=Z(R)∖{0} be the set of non-zero zero-divisors of R. The zero-divisor graph of R, denoted by Γ(R), is a simple graph whose vertex set is Z*(R) and each pair of vertices in Z*(R) are adjacent when their product is 0. In this article, we find the structure and Laplacian spectrum of the zero-divisor graphs Γ(Zn) for n=pN1qN2, where p<q are primes and N1,N2 are positive integers.

The spectra of a new join of graphs

2018 ◽  
Vol 10 (06) ◽  
pp. 1850074 ◽  
Author(s):  
Somnath Paul
Keyword(s):  
Laplacian Spectrum ◽  
Cospectral Graphs ◽  
Signless Laplacian Spectrum ◽  
Signless Laplacian ◽  
Join Of Graphs ◽  
Disjoint Sets

Let [Formula: see text] and [Formula: see text] be three graphs on disjoint sets of vertices and [Formula: see text] has [Formula: see text] edges. Let [Formula: see text] be the graph obtained from [Formula: see text] and [Formula: see text] in the following way: (1) Delete all the edges of [Formula: see text] and consider [Formula: see text] disjoint copies of [Formula: see text]. (2) Join each vertex of the [Formula: see text]th copy of [Formula: see text] to the end vertices of the [Formula: see text]th edge of [Formula: see text]. Let [Formula: see text] be the graph obtained from [Formula: see text] by joining each vertex of [Formula: see text] with each vertex of [Formula: see text] In this paper, we determine the adjacency (respectively, Laplacian, signless Laplacian) spectrum of [Formula: see text] in terms of those of [Formula: see text] and [Formula: see text] As an application, we construct infinite pairs of cospectral graphs.

scholarly journals On Q-integral (3,s)-semiregular bipartite graphs

2010 ◽  
Vol 4 (1) ◽  
pp. 167-174 ◽  
Author(s):  
Slobodan Simic ◽  
Zoran Stanic
Keyword(s):  
Bipartite Graphs ◽  
Laplacian Spectrum ◽  
Signless Laplacian Spectrum ◽  
Signless Laplacian

A graph is called Q-integral if its signless Laplacian spectrum consists entirely of integers. We establish some general results regarding signless Laplacians of semiregular bipartite graphs. Especially, we consider those semiregular bipartite graphs with integral signless Laplacian spectrum. In some particular cases we determine the possible Q-spectra and consider the corresponding graphs.

On the signless Laplacian spectral determination of the join of regular graphs

2014 ◽  
Vol 06 (04) ◽  
pp. 1450050
Author(s):  
Lizhen Xu ◽  
Changxiang He
Keyword(s):  
Regular Graph ◽  
Spectral Determination ◽  
Regular Graphs ◽  
Laplacian Spectrum ◽  
Signless Laplacian Spectrum ◽  
Signless Laplacian

Let G be an r-regular graph with order n, and G ∨ H be the graph obtained by joining each vertex of G to each vertex of H. In this paper, we prove that G ∨ K2is determined by its signless Laplacian spectrum for r = 1, n - 2. For r = n - 3, we show that G ∨ K2is determined by its signless Laplacian spectrum if and only if the complement of G has no triangles.

scholarly journals On the Adjacency, Laplacian, and Signless Laplacian Spectrum of Coalescence of Complete Graphs

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
S. R. Jog ◽  
Raju Kotambari
Keyword(s):  
Line Graph ◽  
Laplacian Matrix ◽  
Spectral Graph Theory ◽  
Complete Graphs ◽  
Laplacian Spectrum ◽  
Spectral Graph ◽  
Signless Laplacian Spectrum ◽  
Subdivision Graph ◽  
Laplacian Energy ◽  
Signless Laplacian

Coalescence as one of the operations on a pair of graphs is significant due to its simple form of chromatic polynomial. The adjacency matrix, Laplacian matrix, and signless Laplacian matrix are common matrices usually considered for discussion under spectral graph theory. In this paper, we compute adjacency, Laplacian, and signless Laplacian energy (Qenergy) of coalescence of pair of complete graphs. Also, as an application, we obtain the adjacency energy of subdivision graph and line graph of coalescence from itsQenergy.

Sign in / Sign up

Export Citation Format

Share Document