The power graph of a finite group

Peter Jephson Cameron, Shamik Ghosh

Research output: Contribution to journalArticlepeer-review

106 Citations (Scopus)

Abstract

The power graph of a group is the graph whose vertex set is the group, two elements being adjacent if one is a power of the other. We observe that non-isomorphic finite groups may have isomorphic power graphs, but that finite abelian groups with isomorphic power graphs must be isomorphic. We conjecture that two finite groups with isomorphic power graphs have the same number of elements of each order. We also show that the only finite group whose automorphism group is the same as that of its power graph is the Klein group of order 4.
Original languageEnglish
Pages (from-to)1220-1222
JournalDiscrete Mathematics
Volume311
Issue number3
DOIs
Publication statusPublished - 2011

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