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+).
Ejima, O., AREMU, K., & Audu, A. (2020). Energy of inverse graphs of dihedral and symmetric groups. Journal of the Egyptian Mathematical Society, 28(1), 1-10. doi: 10.1186/s42787-020-00101-8
MLA
O. Ejima; K. O. AREMU; A. Audu. "Energy of inverse graphs of dihedral and symmetric groups", Journal of the Egyptian Mathematical Society, 28, 1, 2020, 1-10. doi: 10.1186/s42787-020-00101-8
HARVARD
Ejima, O., AREMU, K., Audu, A. (2020). 'Energy of inverse graphs of dihedral and symmetric groups', Journal of the Egyptian Mathematical Society, 28(1), pp. 1-10. doi: 10.1186/s42787-020-00101-8
VANCOUVER
Ejima, O., AREMU, K., Audu, A. Energy of inverse graphs of dihedral and symmetric groups. Journal of the Egyptian Mathematical Society, 2020; 28(1): 1-10. doi: 10.1186/s42787-020-00101-8
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