Original Research Article

Article volume = 2021 and issue = 1

Pages: 84–2

Article publication Date: November, 1, 2021

You can download PDF file of the article here: Download

Visited 207 times and downloaded 148 times

# On The Conjugacy Class Graphs of Some Dicyclic Groups

#### Zeinab Foruzanfar, Mehdi Rezaei

Imam Khomeini International University - Buin Zahra Higher Education Center of Engineering and Technology, Qazvin, Iran.

##### Abstract:

Let G be a dicyclic group and (G) be the attached graph related to its conjugacy classes, which is defined as: the vertices of (G) are represented by the non-central conjugacy classes of G and two distinct vertices xG and yG are connected with an edge if (o(x), o(y)) > 1. In this paper, we calculate the clique number and the girth of (G) for dicyclic groups of orders 4p, 8p, 4p2, 4pq and 2m.

##### Keywords:

Dicyclic group, Conjugacy class, Clique number, Girth.

##### References:

- [1] A. Abdollahi, S. Akbari, H. R. Maimani, Non-commuting graph of a group, J. Algebra, 298 (2006), 468–492. 1
- [2] E. A. Bertram, Some applications of graph theory to finite groups, Discrete Math., 44 (1983), 31–43. 1
- [3] Z. Foruzanfar, Z. Mostaghim, Classification of non-solvable groups with a given property, Proc. Math. Sci., 125(1) (2015), 29–36. 1
- [4] G. James, M. Liebeck, Representations and Characters of Groups, Cambridge University Press, 1993. 2.1, 2.2
- [5] A. R. Moghaddamfar, W. J. Shi, W. Zhou, A. R. Zokayi, On non-commuting graph associated with a finite group, Siberian Math. J., 46 (2005), 325–332. 1
- [6] M. Rezaei, Z. Foruzanfar, Classification of solvable groups with a given property, Bull. Iranian Math. Soc., 43(6) (2017), 1791–1800. 1
- [7] Y. Segev, The commuting graph of minimal nonsolvable groups, Geom. Dedicata., 88(13) (2001), 55–66. 1
- [8] X. You, G. Qian, A new graph related to conjugacy classes of finite groups, Chinese Ann. Math. Ser. A, 28(5) (2007), 631–636. 1

##### Cite this article as:

- Zeinab Foruzanfar, Mehdi Rezaei, On The Conjugacy Class Graphs of Some Dicyclic Groups, Communications in Combinatorics, Cryptography & Computer Science, 2021(1), PP.84–2, 2021
- Export citation to BibTeX