Results 51 to 60 of about 7,385 (154)

Lower and Upper Acyclicities on Unitary Cayley Graphs of Finite Commutative Rings

European Journal of Pure and Applied Mathematics
A unitary Cayley graph $\Gamma_n$ of a finite cyclic ring $\mathbb{Z}_n$ is a graph with vertex set $\mathbb{Z}_n$ and two vertices $x$ and $y$ are adjacent if and only if $x-y$ is a unit in $\mathbb{Z}_n$ or equivalently, $\gcd(x-y,n)=1$.
Denpong Pongpipat, Nuttawoot Nupo
semanticscholar   +1 more source

Gutman Index and Harary Index of Unitary Cayley Graphs

International journal of engineering and technology, 2018
In this paper, we determine the Gutman Index and Harary Index of Unitary Cayley Graphs. The Unitary Cayley Graph Xn is the graph with vertex set  V(Xn) ={u|u∈ Zn} and edge set {uv|gcd(u−v, n) = 1 and u, v ∈ Zn }, where Zn ={0,1,...,n−1}.
Roshan Sara Philipose, B SarasijaP
semanticscholar   +1 more source

Spectral Properties of Unitary Cayley Graphs of Finite Commutative Rings [PDF]

The Electronic Journal of Combinatorics, 2012
Let $R$ be a finite commutative ring. The unitary Cayley graph of $R$, denoted $G_R$, is the graph with vertex set $R$ and edge set $\left\{\{a,b\}:a,b\in R, a-b\in R^\times\right\}$, where $R^\times$ is the set of units of $R$. An $r$-regular graph is Ramanujan if the absolute value of every eigenvalue of it other than $\pm r$ is at most $2\sqrt{r-1}$.
Liu, Xiaogang, Zhou, Sanming
openaire   +3 more sources

Adjacency Algebra of Unitary Cayley Graph

, 2017
8 ...
openaire   +2 more sources

A refinement of the unit and unitary Cayley graphs of a finite ring

, 2016
Let R be a finite commutative ring with nonzero identity. We define Γ(R) to be the graph with vertex set R in which two distinct vertices x and y are adjacent if and only if there exists a unit element u of R such that x + uy is a unit of R.
A. Naghipour, M. Rezagholibeigi
semanticscholar   +1 more source

On Restricted Unitary Cayley Graphs and Symplectic Transformations Modulo $n$ [PDF]

The Electronic Journal of Combinatorics, 2010
We present some observations on a restricted variant of unitary Cayley graphs modulo $n$, and implications for a decomposition of elements of symplectic operators over the integers modulo $n$. We define quadratic unitary Cayley graphs $G_n$, whose vertex set is the ring ${\Bbb Z}_n$, and where residues $a,b$ modulo $n$ are adjacent if and only if ...
openaire   +4 more sources

A CLASSIFICATION OF RAMANUJAN COMPLEMENTS OF UNITARY CAYLEY GRAPHS

, 2017
The unitary Cayley graph on n vertices, Xn, has vertex set Zn, where two vertices a and b are connected by an edge if and only if they differ by a multiplicative unit modulo n, i.e. gcd(ab, n) = 1. A k-regular graph X is Ramanujan if and only if λ(X) ≤ 2
R. Safakish, S. Mehry
semanticscholar   +1 more source

Eigenspaces of Hamming graphs and unitary Cayley graphs

Ars Mathematica Contemporanea, 2010
In this work, the eigenspaces of unitary Cayley graphs and certain Hamming graphs are considered. It is shown that these graph classes are closely related and admit particularly simple eigenspace bases for all eigenvalues, namely bases containing vectors only with entries from the set {0, 1, −1}.
openaire   +2 more sources

Eigenvalues of unitary Cayley graph of matrix algebras and its subconstituents

, 2023
Jitsupat Rattanakangwanwong
semanticscholar   +1 more source

On the unitary Cayley graphs of matrix algebras

Linear Algebra and its Applications, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kiani, Dariush, Mollahajiaghaei, Mohsen
openaire   +1 more source