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THE GROUP OF GRAPH AUTOMORPHISMS OVER A MATRIX RING
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 Title & Authors
THE GROUP OF GRAPH AUTOMORPHISMS OVER A MATRIX RING
Park, Sang-Won; Han, Jun-Cheol;
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 Abstract
Let R = be the ring of all 2 by 2 matrices over a finite field F, X the set of all nonzero, nonunits of R and G the group of all units of R. After investigating some properties of orbits under the left (and right) regular action on X by G, we show that the graph automorphisms group of (the zero-divisor graph of R) is isomorphic to the symmetric group of degree |F|+1.
 Keywords
zero-divisor graph;left (resp. right) regular action;orbit;graph automorphisms group;
 Language
English
 Cited by
1.
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Isomorphisms between Jacobson graphs, Rendiconti del Circolo Matematico di Palermo (1952 -), 2014, 63, 2, 277  crossref(new windwow)
4.
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5.
Automorphism Group of the Rank-decreasing Graph Over the Semigroup of Upper Triangular Matrices, Communications in Algebra, 2016, 44, 9, 4088  crossref(new windwow)
6.
A note on automorphisms of the zero-divisor graph of upper triangular matrices, Linear Algebra and its Applications, 2015, 465, 214  crossref(new windwow)
7.
The group of automorphisms of a zero-divisor graph based on rank one upper triangular matrices, Linear Algebra and its Applications, 2014, 460, 242  crossref(new windwow)
8.
AUTOMORPHISMS OF THE ZERO-DIVISOR GRAPH OVER 2 × 2 MATRICES, Journal of the Korean Mathematical Society, 2016, 53, 3, 519  crossref(new windwow)
9.
Automorphism group of an ideal-relation graph over a matrix ring, Linear and Multilinear Algebra, 2016, 64, 2, 309  crossref(new windwow)
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