Energy of inverse graphs of dihedral and symmetric groups | ||||
| Journal of the Egyptian Mathematical Society | ||||
| Volume 28, Issue 1, June 2020, Page 1-10 PDF (605.91 K) | ||||
| DOI: 10.1186/s42787-020-00101-8 | ||||
 View on SCiNiTO | ||||
| Authors | ||||
| O. Ejima; K. O. AREMU; A. Audu | ||||
| Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Nigeria | ||||
| Abstract | ||||
| Let (G, ∗) be a finite group and S = {x ∈ G|x = x−1} be a subset of G containing its non-self invertible elements. The inverse graph of G denoted by (G) is a graph whose set of vertices coincides with G such that two distinct vertices x and y are adjacent if either x ∗ y ∈ S or y ∗ x ∈ S. In this paper, we study the energy of the dihedral and symmetric groups, we show that if G is a finite non-abelian group with exactly two non-self invertible elements, then the associated inverse graph (G) is never a complete bipartite graph. Furthermore, we establish the isomorphism between the inverse graphs of a subgroup Dp of the dihedral group Dn of order 2p and subgroup Sk of the symmetric groups Sn of order k! such that 2p = n! (p, n, k ≥ 3 and p, n, k ∈ Z+). | ||||
| Keywords | ||||
| Inverse graphs; Energy of graphs; Eigenvalues; Adjacency matrix; Finite groups; Graph of finite groups | ||||
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