Zaid, N. and Sarmin, N. H. and Khasraw, S. M. S. and Gambo, I. and Omar Zai, N. A. F. (2021) The perfect codes of commuting zero divisor graph of some matrices of dimension two. In: 28th Simposium Kebangsaan Sains Matematik, SKSM 2021, 28 July 2021  29 July 2021, Kuantan, Pahang, Virtual.

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Official URL: http://dx.doi.org/10.1088/17426596/1988/1/012070
Abstract
The study of graph properties has gathered many attentions in the past years. The graph properties that are commonly studied include the chromatic number, the clique number and the domination number of a finite graph. In this study, a type of graph properties, which is the perfect code is studied. The perfect code is originally used in coding theory, then extended to other fields including graph theory. Hence, in this paper, the perfect code is determined for the commuting zero divisor graphs of some finite rings of matrices. First, the commuting zero divisor graph of the finite rings of matrices is constructed where its vertices are all zero divisors of the ring and two distinct vertices, say x and y, are adjacent if and only if xy = yx = 0. Then, from the vertex set of the graph, the neighborhood elements of the vertices are determined in order to compute the perfect codes of the graph.
Item Type:  Conference or Workshop Item (Paper) 

Uncontrolled Keywords:  computer programming, matrix algebra 
Subjects:  Q Science > QA Mathematics 
Divisions:  Science 
ID Code:  95666 
Deposited By:  Narimah Nawil 
Deposited On:  31 May 2022 13:04 
Last Modified:  31 May 2022 13:04 
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