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- W3194856861 abstract "Let G be a finite group, the associated identity-power graph Γ (G) is a graph whose vertices V (Γ(G)) are precisely the elements of G and two distinct vertices x,y create the oriented edge (x, y) if and only if xy=e or yx=e (where e is the identity of the group G) and either x=yn or y=xn for some n € N. We investigate some algebraic properties and combinatorial structures of the identity-power graph Γ (G) and show that the graph Γ(G) of a finite group G, is never complete. We also show that if every element x in a finite group G has a unique inverse y € G, and then the identity-power graph of G is acyclic. Furthermore, we show that the size of the identity-power graph Γ (M) of a permutation group M is given by. Where π € M and I (π) is the set of involutions in M." @default.
- W3194856861 created "2021-08-30" @default.
- W3194856861 creator A5016268705 @default.
- W3194856861 date "2021-01-01" @default.
- W3194856861 modified "2023-09-23" @default.
- W3194856861 title "On the Identity-Power Graphs of Finite Groups" @default.
- W3194856861 doi "https://doi.org/10.37421/2090-0902.2021.s2.346" @default.
- W3194856861 hasPublicationYear "2021" @default.
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