Permanents of Hexagonal and Armchair Chains
The permanent is important invariants of a graph with some applications in physics. If G is a graph with adjacency matrix A=aij, then the permanent of A is defined as permA=∑σ∈Sn∏i=1naiσi, where Sn denotes the symmetric group on n symbols. In this paper, the general form of the adjacency matrices of...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2022/7786922 |
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| author | O. Nekooei H. Barzegar A. R. Ashrafi |
| author_facet | O. Nekooei H. Barzegar A. R. Ashrafi |
| author_sort | O. Nekooei |
| collection | DOAJ |
| description | The permanent is important invariants of a graph with some applications in physics. If G is a graph with adjacency matrix A=aij, then the permanent of A is defined as permA=∑σ∈Sn∏i=1naiσi, where Sn denotes the symmetric group on n symbols. In this paper, the general form of the adjacency matrices of hexagonal and armchair chains will be computed. As a consequence of our work, it is proved that if Gk and Hk denote the hexagonal and armchair chains, respectively, then permAG1=4, permAGk=k+12, k≥2, and permAHk=4k with k≥1. One question about the permanent of a hexagonal zig-zag chain is also presented. |
| format | Article |
| id | doaj-art-495d4e02a5ee40ad8ae3dd64e2bb0e5b |
| institution | Kabale University |
| issn | 1687-0425 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-495d4e02a5ee40ad8ae3dd64e2bb0e5b2025-02-03T06:13:05ZengWileyInternational Journal of Mathematics and Mathematical Sciences1687-04252022-01-01202210.1155/2022/7786922Permanents of Hexagonal and Armchair ChainsO. Nekooei0H. Barzegar1A. R. Ashrafi2Department of MathematicsDepartment of MathematicsDepartment of Pure MathematicsThe permanent is important invariants of a graph with some applications in physics. If G is a graph with adjacency matrix A=aij, then the permanent of A is defined as permA=∑σ∈Sn∏i=1naiσi, where Sn denotes the symmetric group on n symbols. In this paper, the general form of the adjacency matrices of hexagonal and armchair chains will be computed. As a consequence of our work, it is proved that if Gk and Hk denote the hexagonal and armchair chains, respectively, then permAG1=4, permAGk=k+12, k≥2, and permAHk=4k with k≥1. One question about the permanent of a hexagonal zig-zag chain is also presented.http://dx.doi.org/10.1155/2022/7786922 |
| spellingShingle | O. Nekooei H. Barzegar A. R. Ashrafi Permanents of Hexagonal and Armchair Chains International Journal of Mathematics and Mathematical Sciences |
| title | Permanents of Hexagonal and Armchair Chains |
| title_full | Permanents of Hexagonal and Armchair Chains |
| title_fullStr | Permanents of Hexagonal and Armchair Chains |
| title_full_unstemmed | Permanents of Hexagonal and Armchair Chains |
| title_short | Permanents of Hexagonal and Armchair Chains |
| title_sort | permanents of hexagonal and armchair chains |
| url | http://dx.doi.org/10.1155/2022/7786922 |
| work_keys_str_mv | AT onekooei permanentsofhexagonalandarmchairchains AT hbarzegar permanentsofhexagonalandarmchairchains AT arashrafi permanentsofhexagonalandarmchairchains |