The Complement of Cubic Power Graph of Dihedral Group

Pankaj Rana; Amit Sehgal; Pooja Bhatia; Pavinder Yadav

doi:10.22342/jims.v32i4.2310

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Pankaj Rana ⁽¹⁾ , Amit Sehgal ⁽²⁾ , Pooja Bhatia ⁽³⁾ , Pavinder Yadav ⁽⁴⁾

(1) Department of Mathematics, Baba Mastnath University, India,

(2) Department of Mathematics, Pt. Neki Ram Sharma Government College, India,

(3) Department of Mathematics, Baba Mastnath University, India,

(4) School of Computer Science, University of Petroleum and Energy Studies, India

https://doi.org/10.22342/jims.v32i4.2310

Issue
Vol. 32 No. 4 (2026): December

Keywords:

Cubic power graph, Dihedral group,, Matching number, Degree of vertex, Chromatic number

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Abstract

The complement of cubic power graph of dihedral group Dn with identity element e, CCPG(Dn) is a simple, undirected and finite graph having vertices pair x,y \in Dn adjacent if and only if there exists no element z \in Dn such that xy=z^3 or yx=z^3 with z^3 \neq e. This research explores the representation of the complement of cubic power graph of Dn structure by giving the explicit formula to derive its structure and structural characteristics in particular the matching number, independence number, chromatic number, girth, clique, vertex degree, domination number, etc.

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Authors

Pankaj Rana

Department of Mathematics, Baba Mastnath University

pankajrana2034@gmail.com (Primary Contact)

Amit Sehgal

Department of Mathematics, Pt. Neki Ram Sharma Government College

Pooja Bhatia

Department of Mathematics, Baba Mastnath University

Pavinder Yadav

School of Computer Science, University of Petroleum and Energy Studies

Rana, P., Sehgal, A., Bhatia, P., & Yadav, P. The Complement of Cubic Power Graph of Dihedral Group. Journal of the Indonesian Mathematical Society, 32(4), 2310. https://doi.org/10.22342/jims.v32i4.2310