Physical Mathematics

Department of Mathematics, Usmanu Danfodiyo, University Sokoto, P.M.B. 2346 Sokoto, Nigeria

Publications

• Research Article   
  On the Identity-Power Graphs of Finite Groups
  Author(s): Abor Isa Garba*, MS Magami and O Ejima
  
  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 &pi.. Read More»
  DOI: 10.37421/2090-0902.2021.s2.346

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