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Tijjani, Bilkisu
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Graph Energy of Non-Coprime Graphs for Some Finite Non-abelian Groups Suleiman, Aliyu; Ibrahim Kiri, Aliyu; Tijjani, Bilkisu
Indonesian Journal of Mathematics and Applications Vol. 4 No. 1 (2026): Indonesian Journal of Mathematics and Applications
Publisher : Universitas Brawijaya

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21776/ub.ijma.2026.004.01.3

Abstract

In this paper, we study the Laplacian energy and Seidel energy of the non-coprime graphs for the dihedral group $D_n$, $n \geq 3$, $n = p^r$, where $p$ is prime and $r \in \mathbb{Z}^+$, and the generalized quaternion $Q_{4n}$, $n \geq 2$. The investigation starts by obtaining the spectrum for the graphs and then generalizing the formulae for computing the respective energies. It is shown that the Seidel energy for the non-coprime graph for a dihedral group when $n = 2^r$, $r > 1$, is less than the Laplacian energy for the same graph; this is also true for the generalized quaternion. Furthermore, the Seidel energy for the non-coprime graph for a dihedral group $D_n$ when $n = 2^r$, $r > 1$, is the same as the adjacency energy of the same graph for the same group.
Co-Authors Ibrahim Kiri, Aliyu Suleiman, Aliyu