# Szeged and Padmakar-Ivan Energies of Non-Commuting Graph for Dihedral Groups

## DOI:

https://doi.org/10.11113/mjfas.v20n5.3629## Keywords:

Szeged matrix, Padmakar-Ivan matrix, non-commuting graph, dihedral group.## Abstract

The graph can represent the molecule structure and the -electron energy derives the concept of graph energy. The graph also can be related to the groups or rings as its vertex set. The non-commutative graph is a type of graph whose construction is determined by the structure of a group. This paper focuses on the energy of the non-commuting graph for dihedral groups using the Szeged and Padmakar-Ivan matrices. Both matrices are constructed based on the distance between two vertices in the graph. The eigenvalues of these matrices lead to the formulation of the graph's energy values. Interestingly, the energies obtained are equal to twice the spectral radius and are hyperenergetic.

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