The perfect codes of commuting zero divisor graph of some matrices of dimension two

Autor:	Ibrahim Gambo, Nor Haniza Sarmin, Nur Athirah Farhana Omar Zai, Sanhan Muhammad Salih Khasraw, Nurhidayah Zaid
Rok vydání:	2021
Předmět:	Combinatorics History Ring (mathematics) Domination analysis Hamming bound Dimension (graph theory) Graph theory Graph property Zero divisor Computer Science Applications Education Mathematics Vertex (geometry)
Zdroj:	Journal of Physics: Conference Series. 1988:012070
ISSN:	1742-6596 1742-6588
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::edefdcfe6a7da3319926e342d790f7e3 https://doi.org/10.1088/1742-6596/1988/1/012070 Zobrazit plný text záznamu