Results 41 to 50 of about 122 (118)
On the Unitary Cayley Graph of a Finite Ring [PDF]
The Electronic Journal of Combinatorics, 2009 We study the unitary Cayley graph associated to an arbitrary finite ring, determining precisely its diameter, girth, eigenvalues, vertex and edge connectivity, and vertex and edge chromatic number. We also compute its automorphism group, settling a question of Klotz and Sander. In addition, we classify all planar graphs and perfect graphs within this
Akhtar, Reza +6 more
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Valuations, completions, and hyperbolic actions of metabelian groups
Journal of the London Mathematical Society, Volume 109, Issue 6, June 2024.Abstract Actions on hyperbolic metric spaces are an important tool for studying groups, and so it is natural, but difficult, to attempt to classify all such actions of a fixed group. In this paper, we build strong connections between hyperbolic geometry and commutative algebra in order to classify the cobounded hyperbolic actions of numerous metabelian
Carolyn R. Abbott +2 more
wiley +1 more source
Generalized resolvents and spectrum for a certain class of perturbed symmetric operators
Journal of Applied Mathematics, Volume 2005, Issue 1, Page 81-92, 2005., 2005 The generalized resolvents for a certain class of perturbed symmetric operators with equal and finite deficiency indices are investigated. Using the WeinsteinโAronszajn formula, we give a classification of the spectrum.
A. Hebbeche
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State Transfer on Unitary Cayley Graphs and Quadratic Unitary Cayley Graphs
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Kalita, Akash, Bhattacharjya, Bikash
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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
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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 ...
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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 andย admit particularly simple eigenspace bases for all eigenvalues, namely bases containing vectors only with entries from the set {0, 1, โ1}.
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Status Sombor Indices of Unitary Cayley Graph
Indian Journal Of Science And TechnologyObjectives: The objective of the study is to obtain the values of status Sombor indices for the unitary Cayley graph. Methods: The unitary Cayley graph ๐๐ has vertex set ๐๐ = {0, 1, 2, ...๐ โ 1}. Vertices a, and b are adjacent, if ๐๐๐(๐ โ ๐, ๐) = 1. The status ๐ (๐ข) of a vertex u in a graph, G is the sum of distances of all other vertices from u in ๐บ ...
Syeda Asma Kauser, Mashaer Alsaeedi
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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
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