IJPAM: Volume 109, No. 2 (2016)

THE ORBIT GRAPH OF METACYCLIC
2-GROUPS OF NEGATIVE TYPE

Mustafa Anis El-Sanfaz$^1$, Nor Haniza Sarmin$^2$, Sanaa Mohamed Saleh Omer$^3$
$^{1,3}$Department of Mathematics
Faculty of Science
University of Benghazi
Benghazi, LIBYA
$^{1,2}$Department of Mathematical Sciences
Faculty of Science
Universiti Teknologi Malaysia
Johor Bahru, MALAYSIA


Abstract. In this paper, let $G$ be a metacyclic 2-group of negative type of class two and class at least three. Let $\Omega$ be the set of all subsets of all commuting elements of size two in the form of $(a, b)$, where $a$ and $b$ commute and $\vert a\vert=\vert b\vert=2$. The orbit graph is a graph whose vertices are non-central orbits under group action of $G$ on $\Omega$. In this paper, the orbit graph of metacyclic 2-groups of negative type of nilpotency class two and class at least three is determined. Some graph properties are also provided.

Received: August 18, 2015

AMS Subject Classification: 20P05, 20B40, 97K30

Key Words and Phrases: commutativity degree, graph theory, orbit graph, group action

Download paper from here.



DOI: 10.12732/ijpam.v109i2.6 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 109
Issue: 2
Pages: 235 - 244


Google Scholar; DOI (International DOI Foundation); WorldCAT.

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).