Graph coloring using commuting order product prime graph
The concept of graph coloring has become a very active field of research that enhances many practical applications and theoretical challenges. Various methods have been applied in carrying out this study. Let G be a finite group. In this paper, we introduce a new graph of groups, which is a commutin...
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my.utm.905992021-04-30T14:55:21Z http://eprints.utm.my/id/eprint/90599/ Graph coloring using commuting order product prime graph Bello, Muhammed Mohd. Ali, Nor Muhainiah Isah, Surajo Ibrahim QA Mathematics The concept of graph coloring has become a very active field of research that enhances many practical applications and theoretical challenges. Various methods have been applied in carrying out this study. Let G be a finite group. In this paper, we introduce a new graph of groups, which is a commuting order product prime graph of finite groups as a graph having the elements of G as its vertices and two vertices are adjacent if and only if they commute and the product of their order is a prime power. This is an extension of the study for order product prime graph of finite groups. The graph’s general presentations on dihedral groups, generalized quaternion groups, quasi-dihedral groups, and cyclic groups have been obtained in this paper. Moreover, the commuting order product prime graph on these groups has been classified as connected, complete, regular, or planar. These results are used in studying various and recently introduced chromatic numbers of graphs. International Scientific Research Publications 2020-10 Article PeerReviewed application/pdf en http://eprints.utm.my/id/eprint/90599/1/NorMuhainiahMohd2020_GraphColoringUsingCommutingOrderProduct.pdf Bello, Muhammed and Mohd. Ali, Nor Muhainiah and Isah, Surajo Ibrahim (2020) Graph coloring using commuting order product prime graph. Journal of Mathematics and Computer Science, 23 (2). pp. 155-169. ISSN 2008-949X http://dx.doi.org/10.22436/jmcs.023.02.08 DOI:10.22436/jmcs.023.02.08 |
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QA Mathematics Bello, Muhammed Mohd. Ali, Nor Muhainiah Isah, Surajo Ibrahim Graph coloring using commuting order product prime graph |
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The concept of graph coloring has become a very active field of research that enhances many practical applications and theoretical challenges. Various methods have been applied in carrying out this study. Let G be a finite group. In this paper, we introduce a new graph of groups, which is a commuting order product prime graph of finite groups as a graph having the elements of G as its vertices and two vertices are adjacent if and only if they commute and the product of their order is a prime power. This is an extension of the study for order product prime graph of finite groups. The graph’s general presentations on dihedral groups, generalized quaternion groups, quasi-dihedral groups, and cyclic groups have been obtained in this paper. Moreover, the commuting order product prime graph on these groups has been classified as connected, complete, regular, or planar. These results are used in studying various and recently introduced chromatic numbers of graphs. |
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Article |
author |
Bello, Muhammed Mohd. Ali, Nor Muhainiah Isah, Surajo Ibrahim |
author_facet |
Bello, Muhammed Mohd. Ali, Nor Muhainiah Isah, Surajo Ibrahim |
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Bello, Muhammed |
title |
Graph coloring using commuting order product prime graph |
title_short |
Graph coloring using commuting order product prime graph |
title_full |
Graph coloring using commuting order product prime graph |
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Graph coloring using commuting order product prime graph |
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Graph coloring using commuting order product prime graph |
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graph coloring using commuting order product prime graph |
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International Scientific Research Publications |
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2020 |
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http://eprints.utm.my/id/eprint/90599/1/NorMuhainiahMohd2020_GraphColoringUsingCommutingOrderProduct.pdf http://eprints.utm.my/id/eprint/90599/ http://dx.doi.org/10.22436/jmcs.023.02.08 |
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