Open AccessThe Generalized Power Graph of a Finite Group
Author(s) -
Xuanlong Ma,
Ruiqin Fu
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1237/2/022040
Subject(s) - combinatorics , mathematics , vertex transitive graph , symmetric graph , vertex (graph theory) , graph , discrete mathematics , voltage graph , edge transitive graph , line graph
Graphs associated with groups and other algebraic structures have been actively investigated, since they have valuable applications in data mining. For a finite group G, let Γ G be the graph with the non-identity elements of G as the vertex set, and two vertices are adjacent if they respectively lie in two conjugate proper subgroups of G. Γ G is called the generalized power graph with respect to G. This paper explores how the graph theoretical properties of Γ G can affect on the group theoretical properties of G.