Unitary invertible graphs of finite rings
نویسندگان
چکیده
منابع مشابه
Unitary Cayley Graphs for Finite Rings
Given an integer n, one defines the unitary Cayley graph, denoted Cay(Zn,Zn), to be the graph whose vertex set is Zn, the integers modulo n, with an edge between two vertices x, y if x− y is a unit in (the ring) Zn. Unitary Cayley graphs have been studied as objects of independent interest (see, for example, [3], [2], [7], [8], [9]) but are of particular relevance in the study of graph represen...
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Let R be a finite commutative ring. The unitary Cayley graph of R, denoted GR, is the graph with vertex set R and edge set {{a, b} : a, b ∈ R, a− b ∈ R×}, where R× is the set of units of R. An r-regular graph is Ramanujan if the absolute value of every eigenvalue of it other than ±r is at most 2 √ r − 1. In this paper we give a necessary and sufficient condition for GR to be Ramanujan, and a ne...
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Let $R$ be a ring (not necessarily commutative) with nonzero identity. We define $Gamma(R)$ to be the graph with vertex set $R$ in which two distinct vertices $x$ and $y$ are adjacent if and only if there exist unit elements $u,v$ of $R$ such that $x+uyv$ is a unit of $R$. In this paper, basic properties of $Gamma(R)$ are studied. We investigate connectivity and the girth of $Gamma(R)$, where $...
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We investigate spectra of Cayley graphs for the Heisenberg group over Þnite rings Z/pZ, where p is a prime. Emphasis is on graphs of degree four. We show that for odd p there is only one such connected graph up to isomorphism. When p = 2, there are at most two isomorphism classes. We study the spectra using representations of the Heisenberg group. This allows us to produce histograms and butter...
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ژورنال
عنوان ژورنال: Discussiones Mathematicae - General Algebra and Applications
سال: 2021
ISSN: 1509-9415,2084-0373
DOI: 10.7151/dmgaa.1350