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http://dx.doi.org/10.4134/JKMS.2011.48.2.301

THE GROUP OF GRAPH AUTOMORPHISMS OVER A MATRIX RING  

Park, Sang-Won (DEPARTMENT OF MATHEMATICS DONG-A UNIVERSITY)
Han, Jun-Cheol (DEPARTMENT OF MATHEMATICS EDUCATION PUSAN NATIONAL UNIVERSITY)
Publication Information
Journal of the Korean Mathematical Society / v.48, no.2, 2011 , pp. 301-309 More about this Journal
Abstract
Let R = $Mat_2(F)$ 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 $\Gamma(R)$ (the zero-divisor graph of R) is isomorphic to the symmetric group $S_{|F|+1}$ of degree |F|+1.
Keywords
zero-divisor graph; left (resp. right) regular action; orbit; graph automorphisms group;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
Times Cited By Web Of Science : 0  (Related Records In Web of Science)
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