A SURVEY ON THE AUTOMORPHISM GROUPS OF THE COMMUTING GRAPHS AND POWER GRAPHS

Mahsa Mirzargar

DOI Number
https://doi.org/10.22190/FUMI1904729M
First page
729
Last page
743

Abstract


Let G be a nite group. The power graph P(G) of a group G is the graph
whose vertex set is the group elements and two elements are adjacent if one is a power of the other. The commuting graph \Delta(G) of a group G, is the graph whose vertices are the group elements, two of them joined if they commute. When the vertex set is G-Z(G), this graph is denoted by \Gamma(G). Since the results based on the automorphism group of these kinds of graphs are so sporadic, in this paper, we give a survey of all results on the automorphism group of power graphs and commuting graphs obtained in the literature.


Keywords

Finite group; graph; vertex set; commuting graph; automorphism groups.

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References


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DOI: https://doi.org/10.22190/FUMI1904729M

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