Decomposition of hypercube graphs into paths and cycles having k edges
For an even graph G and positive integer p, q, and k, the pair (p, q) is an admissible pair if [Formula: see text]. If a graph G admits a decomposition into p copies of [Formula: see text], the path of length k, and q copies of Ck, the cycle of length k, for every admissible pair (p, q), then G has...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2025-01-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
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| Online Access: | https://www.tandfonline.com/doi/10.1080/09728600.2024.2444564 |
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| author | D. Saranya S. Jeevadoss V. Nalini V. Chitra |
| author_facet | D. Saranya S. Jeevadoss V. Nalini V. Chitra |
| author_sort | D. Saranya |
| collection | DOAJ |
| description | For an even graph G and positive integer p, q, and k, the pair (p, q) is an admissible pair if [Formula: see text]. If a graph G admits a decomposition into p copies of [Formula: see text], the path of length k, and q copies of Ck, the cycle of length k, for every admissible pair (p, q), then G has a [Formula: see text]-decomposition. In this paper, we give necessary and sufficient conditions for the existence of a [Formula: see text]-decomposition of n-dimensional hypercube graphs Qn when n is even, [Formula: see text] and [Formula: see text] |
| format | Article |
| id | doaj-art-1938efec77794f40a91dd0f0d8b855b2 |
| institution | Kabale University |
| issn | 0972-8600 2543-3474 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | AKCE International Journal of Graphs and Combinatorics |
| spelling | doaj-art-1938efec77794f40a91dd0f0d8b855b22025-01-17T18:15:14ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002543-34742025-01-0111110.1080/09728600.2024.2444564Decomposition of hypercube graphs into paths and cycles having k edgesD. Saranya0S. Jeevadoss1V. Nalini2V. Chitra3Department of Mathematics, Bannari Amman Institute of Technology, Sathyamangalam, Erode, Tamil Nadu, India;Department of Applied Mathematics and Computational Sciences, PSG College of Technology, Coimbatore, Tamil Nadu, India;Department of Mathematics, Dr. N. G. P Institute of Technology, Coimbatore, Tamil Nadu, India;Department of Mathematics, PSG Institute of Technology and Applied Research, Coimbatore, Tamil Nadu, IndiaFor an even graph G and positive integer p, q, and k, the pair (p, q) is an admissible pair if [Formula: see text]. If a graph G admits a decomposition into p copies of [Formula: see text], the path of length k, and q copies of Ck, the cycle of length k, for every admissible pair (p, q), then G has a [Formula: see text]-decomposition. In this paper, we give necessary and sufficient conditions for the existence of a [Formula: see text]-decomposition of n-dimensional hypercube graphs Qn when n is even, [Formula: see text] and [Formula: see text]https://www.tandfonline.com/doi/10.1080/09728600.2024.2444564Cyclegraph decompositionhypercube graphpathregular bipartite graph05C51 |
| spellingShingle | D. Saranya S. Jeevadoss V. Nalini V. Chitra Decomposition of hypercube graphs into paths and cycles having k edges AKCE International Journal of Graphs and Combinatorics Cycle graph decomposition hypercube graph path regular bipartite graph 05C51 |
| title | Decomposition of hypercube graphs into paths and cycles having k edges |
| title_full | Decomposition of hypercube graphs into paths and cycles having k edges |
| title_fullStr | Decomposition of hypercube graphs into paths and cycles having k edges |
| title_full_unstemmed | Decomposition of hypercube graphs into paths and cycles having k edges |
| title_short | Decomposition of hypercube graphs into paths and cycles having k edges |
| title_sort | decomposition of hypercube graphs into paths and cycles having k edges |
| topic | Cycle graph decomposition hypercube graph path regular bipartite graph 05C51 |
| url | https://www.tandfonline.com/doi/10.1080/09728600.2024.2444564 |
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