THE GROUP OF GRAPH AUTOMORPHISMS OVER A MATRIX RING

Title & Authors
THE GROUP OF GRAPH AUTOMORPHISMS OVER A MATRIX RING
Park, Sang-Won; Han, Jun-Cheol;

Abstract
Let R = $\small{Mat_2(F)}$ 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 $\small{\Gamma(R)}$ (the zero-divisor graph of R) is isomorphic to the symmetric group $\small{S_{|F|+1}}$ of degree |F|+1.
Keywords
zero-divisor graph;left (resp. right) regular action;orbit;graph automorphisms group;
Language
English
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