Automorphisms of the zero-divisor graph of the ring of all <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>n</mml:mi><mml:mo>×</mml:mo><mml:mi>n</mml:mi></mml:math> matrices over a finite field

Wang, Long

doi:10.1016/j.disc.2016.02.021

Cited by 22 publications

(7 citation statements)

References 20 publications

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“…Recently, the automorphisms of the zero-divisor graph over the matrix ring attracted the attention of researchers (see [9,12,17,20,24]). Also, Feng Xu et al [21], determined all the automorphisms of the intersection graph of ideals over a matrix ring.…”

Section: Introductionmentioning

confidence: 99%

Automorphisms of left Ideal relation graph over full matrix ring

Kumar¹,

Baloda²,

Malhotra³

2022

Preprint

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The left-ideal relation graph on a ring R, denoted by − − → Γ l−i (R), is a directed graph whose vertex set is all the elements of R and there is a directed edge from x to a distinct y if and only if the left ideal generated by x, written as [x], is properly contained in the left ideal generated by y. In this paper, the automorphisms of − − → Γ l−i (R) are characterized, where R is the ring of all n × n matrices over a finite field Fq. The undirected left relation graph, denoted by Γ l−i (Mn(Fq)), is the simple graph whose vertices are all the elements of R and two distinct vertices x, y are adjacent if and only if either [x] ⊂ [y] or [y] ⊂ [x] is considered. Various graph theoretic properties of Γ l−i (Mn(Fq))including connectedness, girth, clique number, etc. are studied.

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Section: Introductionmentioning

confidence: 99%

Automorphisms of left Ideal relation graph over full matrix ring

Kumar¹,

Baloda²,

Malhotra³

2022

Preprint

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“…On the other hand, for the case of S being non-commutative, it seems to the authors that many cases that were dealt with involve matrix rings over finite fields, which, in turn, results in finite ambient zero-divisor graphs. (For example, see [3], [8], [10], and [15].) With somewhat similar but essentially different point of view, in this paper, we are interested in the zero-divisor graph of the matrix ring M 2 (R) for the ring R of algebraic integers in a number field K with [K : Q] ≤ 2.…”

Section: Introductionmentioning

confidence: 99%

The Establishment and Activities of the and Taedongdan, Jeollabuk-do Province

Chang¹,

강사²

2021

JEONBUK SAHAK ; The Jeonbuk Historical Journal

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“…One of the most important object for the graphs related to algebraic structures, is the automorphism group of these graphs. There are many studies about the automorphism groups of the graphs see [3], [7], [10], [11] and [12]. In particular for automorphisms of the graphs related to the vector spaces see [9] and references therein.…”

Section: Introductionmentioning

confidence: 99%

Automorphisms of linear functional graphs over vector spaces

Majidinya¹

2020

Preprint

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Let F q be a finite field with q elements, n ≥ 2 a positive integer, V 0 a n-dimensional vector space over F q and T 0 the set of all linear functionals from V 0 to F q . Let V = V 0 \ {0} and T = T 0 \ {0}. The linear functional graph of V 0 dented by ̥(V), is an undirected bipartite graph, whose vertex set V is partitioned into two sets as V = V ∪ T and two vertices v ∈ V and f ∈ T are adjacent if and only if f sends v to the zero element of F q (i.e. f (v) = 0). In this paper, the structure of all automorphisms of this graph is characterized and formolized. Also the cardinal number of automorphisms group for this graph is determined.

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Automorphisms of the zero-divisor graph of the ring of all n×n matrices over a finite field

Cited by 22 publications

References 20 publications

Automorphisms of left Ideal relation graph over full matrix ring

Automorphisms of left Ideal relation graph over full matrix ring

The Establishment and Activities of the and Taedongdan, Jeollabuk-do Province

Automorphisms of linear functional graphs over vector spaces

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