Topological Indices and Structural Properties of Cubic Power Graph of Dihedral Group

Authors

  • Pankaj Rana Department of Mathematics, Baba Mastnath University, Asthal Bohar, Rohtak-124021(Haryana), India https://orcid.org/0000-0002-5319-932X
  • Amit Sehgal Department of Mathematics, Pt. NRS Govt. College, Rohtak-124001(Haryana), India https://orcid.org/0000-0001-7820-8037
  • Pooja Bhatia Department of Mathematics, Baba Mastnath University, Asthal Bohar, Rohtak-124021(Haryana), India
  • Parvesh Kumar Department of Mathematics, Pt. NRS Govt. College, Rohtak-124001(Haryana), India

DOI:

https://doi.org/10.37256/cm.5120243029

Keywords:

dihedral group, cubic power graph, degree of vertex, chromatic number, matching number, topological indices

Abstract

The cubic power graph of finite group G with identity element e, is an undirected finite, simple graph in which a pair of distinct vertices x, y have an edge iff xy = z3 or yx = z3 for any z Dn with z3e. In this paper, we have studied the structural representation of the cubic power graph of the dihedral group and various structural properties such as clique, girth, vertex degree, chromatic number, independent number, matching number, perfect matching, dominating number, etc. We have also calculated various topological indices such as the Harary index, the first and second Zagreb indices, the Wiener and hyper-Wiener indices, the Schultz index, the harmonic index, the general Randic index, the eccentric connectivity index, the Gutman index, the atomic-bond connectivity index, and the geometricarithmetic index of the cubic power graph of dihedral group Dn when gcd(n, 3) = 1.

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Published

2024-02-29

How to Cite

1.
Rana P, Sehgal A, Bhatia P, Kumar P. Topological Indices and Structural Properties of Cubic Power Graph of Dihedral Group. Contemp. Math. [Internet]. 2024 Feb. 29 [cited 2024 Oct. 14];5(1):761-79. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/3029