Zulkarnain, Athirah and Mat Hassim, Hazzirah Izzati and Sarmin, Nor Haniza and Erfanian, Ahmad (2022) The nonabelian tensor square graph associated to a symmetric group and its perfect code. Mathematics and Statistics, 10 (2). 436 441. ISSN 23322071

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Official URL: http://dx.doi.org/10.13189/ms.2022.100219
Abstract
A set of vertices and edges forms a graph. A graph can be associated with groups using the groups' properties for its vertices and edges. The set of vertices of the graph comprises the elements of the group, while the set of edges of the graph is the properties and requirements for the graph. A nonabelian tensor square graph of a group is defined when its vertex set represents the nontensor centre elements' set of G. Then, two distinguished vertices are connected by an edge if and only if the nonabelian tensor square of these two elements is not equal to the identity of the nonabelian tensor square. This study investigates the nonabelian tensor square graph for the symmetric group of order six. In addition, some properties of this group's nonabelian tensor square graph are computed, including the diameter, the dominating number, and the chromatic number. The perfect code for the nonabelian tensor square graph for a symmetric group of order six is also found in this paper.
Item Type:  Article 

Uncontrolled Keywords:  chromatic number, diameter, graph theory 
Subjects:  Q Science > QA Mathematics 
Divisions:  Science 
ID Code:  98755 
Deposited By:  Narimah Nawil 
Deposited On:  02 Feb 2023 08:23 
Last Modified:  02 Feb 2023 08:23 
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