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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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Let G be a finite group and X be a union of conjugacy classes of G. Define C(G,X) to be the graph with vertex set X and x, y ∈ X (x ≠ y) joined by an edge whenever they commute. In the case that X = G, this graph is named commuting graph of G, denoted by △(G). The aim of this paper is to study the automorphism group of the commuting graph. It is proved that Aut(△(G)) is abelian if and only if |G| ≤ 2 |Aut(△(G))| is of prime power if and only if |G| ≤ 2, and |Aut(△(G))| is square-free if and only if |G| ≤ 3. Some new graphs that are useful in studying the automorphism group of △(G) are presented and their main properties are investigated.
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참고문헌 (15)
참고문헌 신청
A. Abdollahi / 2006 / Non-commuting graph of a group / J. Algebra 298 (2) : 468 ~ 492
A. R. Moghaddamfar / 2005 / On the noncommuting graph associated with a finite group / Siberian Math. J 46 : 325 ~ 332
A. R. Moghaddamfar / 2006 / On noncommutativity graphs / Siberian Math. J 47 : 911 ~ 914
B. H. Neumann / 1976 / A problem of Paul Erd¨os on groups / J. Aust. Math. Soc. Ser. A 21 (4)
D. B. West / 1996 / Introduction to Graph Theory / Prentice Hall. Inc
A. R. Moghaddamfar / 2005 / On the noncommuting graph associated with a finite group / Siberian Math. J 46 : 325 ~ 332
A. R. Moghaddamfar / 2006 / On noncommutativity graphs / Siberian Math. J 47 : 911 ~ 914
B. H. Neumann / 1976 / A problem of Paul Erd¨os on groups / J. Aust. Math. Soc. Ser. A 21 (4)
D. B. West / 1996 / Introduction to Graph Theory / Prentice Hall. Inc
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