Results 21 to 30 of about 122 (118)
On Laplacian spectrum of unitary Cayley graphs [PDF]
Acta Universitatis Sapientiae, Informatica, 2021 Abstract Let R be a commutative ring with unity 1 ≠ 0 and let R× be the set of all unit elements of R. The unitary Cayley graph of R, denoted by GR = Cay(R, R×), is a simple graph whose vertex set is R and there is an edge between two distinct vertices x and y of R if and only if x − y ∈ R×.
Pirzada S., Barati Z., Afkhami M.
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Domination in Cayley graphs: A survey
AKCE International Journal of Graphs and Combinatorics, 2019 Let Ω be a symmetric generating set of a finite group Γ. Assume that (Γ,Ω)be such that Γ=〈Ω〉and Ω satisfies the two conditions C1: the identity element e∉Ω and C2: if a∈Ω, then a−1∈Ω. Given (Γ,Ω)satisfying C1and C2, define a Cayley graph G=Cay(Γ,Ω)with V(
T. Tamizh Chelvam, M. Sivagami
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Polynomials of unitary Cayley graphs
Filomat, 2015 The unitary Cayley graph Xn has the vertex set Zn = {0,1,2,..., n-1} and vertices a and b are adjacent, if and only if gcd(a-b,n) = 1. In this paper, we present some properties of the clique, independence and distance polynomials of the unitary Cayley graphs and generalize some of the results from [W. Klotz, T.
Milan Basic, Aleksandar Ilic
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Unitary Cayley Meet Signed Graphs
Electronic Notes in Discrete Mathematics, 2017 Abstract A signed graph S is a graph in which every edge receive either ‘+’ or ‘-’ called the signs of the edges. The unitary Cayley graph Xn is a graph with vertex set Zn, the integers modulo n, where n is a positive integer greater than 1. Two vertices x1 and x2 are adjacent in the unitary Cayley graph if and only if their difference is in Un ...
Deepa Sinha, Ayushi Dhama
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On the Unitary Cayley Graph of a Ring [PDF]
The Electronic Journal of Combinatorics, 2012 Let $R$ be a ring with identity. The unitary Cayley graph of a ring $R$, denoted by $G_{R}$, is the graph, whose vertex set is $R$, and in which $\{x,y\}$ is an edge if and only if $x-y$ is a unit of $R$. In this paper we find chromatic, clique and independence number of $G_{R}$, where $R$ is a finite ring.
Kiani, Dariush +1 more
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Mathematische Nachrichten, Volume 293, Issue 7, Page 1278-1327, July 2020., 2020 Abstract With a closed symmetric operator A in a Hilbert space H a triple Π={H,Γ0,Γ1} of a Hilbert space H and two abstract trace operators Γ0 and Γ1 from A∗ to H is called a generalized boundary triple for A∗ if an abstract analogue of the second Green's formula holds.
Volodymyr Derkach +2 more
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A Classification of Ramanujan Unitary Cayley Graphs [PDF]
The Electronic Journal of Combinatorics, 2010 The unitary Cayley graph on $n$ vertices, $X_n$, has vertex set ${\Bbb Z}/{n\Bbb Z}$, and two vertices $a$ and $b$ are connected by an edge if and only if they differ by a multiplicative unit modulo $n$, i.e. ${\rm gcd}(a-b,n) = 1$. A $k$-regular graph $X$ is Ramanujan if and only if $\lambda(X) \leq 2\sqrt{k-1}$ where $\lambda(X)$ is the second ...
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Perfect state transfer in unitary Cayley graphs over local rings [PDF]
Transactions on Combinatorics, 2014 In this work, using eigenvalues and eigenvectors of unitary Cayley graphs over finite local rings and elementary linear algebra, we characterize which local rings allowing PST occurring in its unitary Cayley graph.
Yotsanan Meemark , Songpon Sriwongsa
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On unitary Cayley graphs of matrix rings
Discrete Mathematics, 2022 A unitary Cayley graph \(C_R\) of a ring \(R\) is the graph whose vertex set consists of the elements of \(R\) and two vertices \(x\), \(y\) are adjacent if and only if \(x-y\) is a unit of \(R\). The authors of the paper investigate the spectra of the Cayley graphs of matrix rings \(M_n(F_q)\) and \(M_n(R)\), where \(R\) is a finite commutative ring ...
Chen, Bocong, Huang, Jing
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The energy of unitary cayley graphs
Linear Algebra and its Applications, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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