Number of cycles of small length in a graph
AbstractLet G be a simple undirected graph. In this article, we obtain an explicit formula for the number of 8-cycles in G in terms of the entries of its adjacency matrix. We provide new formulae to find the number of cycles of length 4, 5 and 6 in G. When the girth of G is 10 (resp. 12), an explici...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2023-05-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/09728600.2023.2234421 |
| _version_ | 1797691184369369088 |
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| author | Sasmita Barik Sane Umesh Reddy |
| author_facet | Sasmita Barik Sane Umesh Reddy |
| author_sort | Sasmita Barik |
| collection | DOAJ |
| description | AbstractLet G be a simple undirected graph. In this article, we obtain an explicit formula for the number of 8-cycles in G in terms of the entries of its adjacency matrix. We provide new formulae to find the number of cycles of length 4, 5 and 6 in G. When the girth of G is 10 (resp. 12), an explicit formula for the number of cycles of length 10 (resp. 12) is given. New formulae to find the number of paths of length 3, 4 and 5 in G are also obtained. |
| first_indexed | 2024-03-12T02:09:42Z |
| format | Article |
| id | doaj.art-f3f3945d18f74b7388740dc8a1773194 |
| institution | Directory Open Access Journal |
| issn | 0972-8600 2543-3474 |
| language | English |
| last_indexed | 2024-03-12T02:09:42Z |
| publishDate | 2023-05-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | AKCE International Journal of Graphs and Combinatorics |
| spelling | doaj.art-f3f3945d18f74b7388740dc8a17731942023-09-06T14:45:48ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002543-34742023-05-0120213414710.1080/09728600.2023.2234421Number of cycles of small length in a graphSasmita Barik0Sane Umesh Reddy1School of Basic Sciences, IIT Bhubaneswar, Bhubaneswar, IndiaSchool of Basic Sciences, IIT Bhubaneswar, Bhubaneswar, IndiaAbstractLet G be a simple undirected graph. In this article, we obtain an explicit formula for the number of 8-cycles in G in terms of the entries of its adjacency matrix. We provide new formulae to find the number of cycles of length 4, 5 and 6 in G. When the girth of G is 10 (resp. 12), an explicit formula for the number of cycles of length 10 (resp. 12) is given. New formulae to find the number of paths of length 3, 4 and 5 in G are also obtained.https://www.tandfonline.com/doi/10.1080/09728600.2023.2234421Graphadjacency matrixwalkpathcyclegirth |
| spellingShingle | Sasmita Barik Sane Umesh Reddy Number of cycles of small length in a graph AKCE International Journal of Graphs and Combinatorics Graph adjacency matrix walk path cycle girth |
| title | Number of cycles of small length in a graph |
| title_full | Number of cycles of small length in a graph |
| title_fullStr | Number of cycles of small length in a graph |
| title_full_unstemmed | Number of cycles of small length in a graph |
| title_short | Number of cycles of small length in a graph |
| title_sort | number of cycles of small length in a graph |
| topic | Graph adjacency matrix walk path cycle girth |
| url | https://www.tandfonline.com/doi/10.1080/09728600.2023.2234421 |
| work_keys_str_mv | AT sasmitabarik numberofcyclesofsmalllengthinagraph AT saneumeshreddy numberofcyclesofsmalllengthinagraph |