The Harary index of the non-commuting graph for dihedral groups
Assume G is a non-abelian group which consists a set of vertices, V = {v1 , v2, ..., vn} and a set of edges, E = {e1, e2, ..., em} where n and m are the positive integers. The non-commuting graph of G, denoted by ΓG, is the graph of vertex set G−Z(G), whose vertices are non-central elements, in whic...
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my.utm.304912022-02-28T13:26:39Z http://eprints.utm.my/id/eprint/30491/ The Harary index of the non-commuting graph for dihedral groups Alimon, N. I. Sarmin, N. H. Erfanian, A. QA Mathematics Assume G is a non-abelian group which consists a set of vertices, V = {v1 , v2, ..., vn} and a set of edges, E = {e1, e2, ..., em} where n and m are the positive integers. The non-commuting graph of G, denoted by ΓG, is the graph of vertex set G−Z(G), whose vertices are non-central elements, in which Z(G) is the center of G and two distinct vertices are adjacent if and only if they do not commute. In addition, the Harary index of a graph ΓG is the half-sum of the elements in the reciprocal distance of Dij where Dij the distance between vertex i and vertex j. In this paper, the Harary index of the non-commuting graph for dihedral groups is determined and its general formula is developed. SEAMS 2020 Article PeerReviewed Alimon, N. I. and Sarmin, N. H. and Erfanian, A. (2020) The Harary index of the non-commuting graph for dihedral groups. Southeast Asian Bulletin of Mathematics, 44 . pp. 763-768. ISSN 0129-2021 |
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Assume G is a non-abelian group which consists a set of vertices, V = {v1 , v2, ..., vn} and a set of edges, E = {e1, e2, ..., em} where n and m are the positive integers. The non-commuting graph of G, denoted by ΓG, is the graph of vertex set G−Z(G), whose vertices are non-central elements, in which Z(G) is the center of G and two distinct vertices are adjacent if and only if they do not commute. In addition, the Harary index of a graph ΓG is the half-sum of the elements in the reciprocal distance of Dij where Dij the distance between vertex i and vertex j. In this paper, the Harary index of the non-commuting graph for dihedral groups is determined and its general formula is developed. |
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Article |
author |
Alimon, N. I. Sarmin, N. H. Erfanian, A. |
author_facet |
Alimon, N. I. Sarmin, N. H. Erfanian, A. |
author_sort |
Alimon, N. I. |
title |
The Harary index of the non-commuting graph for dihedral groups |
title_short |
The Harary index of the non-commuting graph for dihedral groups |
title_full |
The Harary index of the non-commuting graph for dihedral groups |
title_fullStr |
The Harary index of the non-commuting graph for dihedral groups |
title_full_unstemmed |
The Harary index of the non-commuting graph for dihedral groups |
title_sort |
harary index of the non-commuting graph for dihedral groups |
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SEAMS |
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2020 |
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http://eprints.utm.my/id/eprint/30491/ |
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1726791443622658048 |
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13.160551 |