Generation of strongly regular graphs from quaternary complex Hadamard matrices
A strongly regular graph with parameters (<em>v</em><em>,</em> <em>k, </em>μ, λ)<em> </em>is a regular graph <em>G </em>with <em>v </em>vertices and <em>k </em>degree in which every two adjacent vertices have λ commo...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Faculty of Science, University of Peradeniya, Sri Lanka
2018-03-01
|
| Series: | Ceylon Journal of Science |
| Subjects: | |
| Online Access: | https://cjs.sljol.info/articles/7488 |
| _version_ | 1811193694184800256 |
|---|---|
| author | W. V. Nishadi K. D. E. Dhananjaya A. A. I. Perera P. Gunathilake |
| author_facet | W. V. Nishadi K. D. E. Dhananjaya A. A. I. Perera P. Gunathilake |
| author_sort | W. V. Nishadi |
| collection | DOAJ |
| description | A strongly regular graph with parameters (<em>v</em><em>,</em> <em>k, </em>μ, λ)<em> </em>is a regular graph <em>G </em>with <em>v </em>vertices and <em>k </em>degree in which every two adjacent vertices have λ common neighbors and every two non-adjacent vertices have μ common neighbors. In this paper, we propose an algorithm which can be used to construct strongly regular graphs using quaternary complex Hadamard matrices. The order of the strongly regular graph generated by a quaternary complex Hadamard matrix of order <em>n </em>is 2<em><sup>n</sup></em>. The proposed algorithm has been illustrated by generating a strongly regular graph of order 4 using quaternary complex Hadamard matrix of order 2. Further, higher order strongly regular graphs were tested using Java program. This algorithm could be used to construct strongly regular graphs of order 2<sup>2n</sup>; n∈Z<sup>^+</sup>. |
| first_indexed | 2024-04-12T00:13:54Z |
| format | Article |
| id | doaj.art-855b13ca542948999f7ee9f133f4cdc4 |
| institution | Directory Open Access Journal |
| issn | 2513-2814 2513-230X |
| language | English |
| last_indexed | 2024-04-12T00:13:54Z |
| publishDate | 2018-03-01 |
| publisher | Faculty of Science, University of Peradeniya, Sri Lanka |
| record_format | Article |
| series | Ceylon Journal of Science |
| spelling | doaj.art-855b13ca542948999f7ee9f133f4cdc42022-12-22T03:55:54ZengFaculty of Science, University of Peradeniya, Sri LankaCeylon Journal of Science2513-28142513-230X2018-03-01471656810.4038/cjs.v47i1.74885690Generation of strongly regular graphs from quaternary complex Hadamard matricesW. V. Nishadi0K. D. E. Dhananjaya1A. A. I. Perera2P. Gunathilake3University of Peradeniya, PeradeniyaUniversity of Peradeniya, PeradeniyaUniversity of Peradeniya, PeradeniyaUniversity of Peradeniya, PeradeniyaA strongly regular graph with parameters (<em>v</em><em>,</em> <em>k, </em>μ, λ)<em> </em>is a regular graph <em>G </em>with <em>v </em>vertices and <em>k </em>degree in which every two adjacent vertices have λ common neighbors and every two non-adjacent vertices have μ common neighbors. In this paper, we propose an algorithm which can be used to construct strongly regular graphs using quaternary complex Hadamard matrices. The order of the strongly regular graph generated by a quaternary complex Hadamard matrix of order <em>n </em>is 2<em><sup>n</sup></em>. The proposed algorithm has been illustrated by generating a strongly regular graph of order 4 using quaternary complex Hadamard matrix of order 2. Further, higher order strongly regular graphs were tested using Java program. This algorithm could be used to construct strongly regular graphs of order 2<sup>2n</sup>; n∈Z<sup>^+</sup>.https://cjs.sljol.info/articles/7488tensor product, simple graphs, k- regular graphs, strongly regular graphs, adjacency matrix, latin squares, cyclic shifting method |
| spellingShingle | W. V. Nishadi K. D. E. Dhananjaya A. A. I. Perera P. Gunathilake Generation of strongly regular graphs from quaternary complex Hadamard matrices Ceylon Journal of Science tensor product, simple graphs, k- regular graphs, strongly regular graphs, adjacency matrix, latin squares, cyclic shifting method |
| title | Generation of strongly regular graphs from quaternary complex Hadamard matrices |
| title_full | Generation of strongly regular graphs from quaternary complex Hadamard matrices |
| title_fullStr | Generation of strongly regular graphs from quaternary complex Hadamard matrices |
| title_full_unstemmed | Generation of strongly regular graphs from quaternary complex Hadamard matrices |
| title_short | Generation of strongly regular graphs from quaternary complex Hadamard matrices |
| title_sort | generation of strongly regular graphs from quaternary complex hadamard matrices |
| topic | tensor product, simple graphs, k- regular graphs, strongly regular graphs, adjacency matrix, latin squares, cyclic shifting method |
| url | https://cjs.sljol.info/articles/7488 |
| work_keys_str_mv | AT wvnishadi generationofstronglyregulargraphsfromquaternarycomplexhadamardmatrices AT kdedhananjaya generationofstronglyregulargraphsfromquaternarycomplexhadamardmatrices AT aaiperera generationofstronglyregulargraphsfromquaternarycomplexhadamardmatrices AT pgunathilake generationofstronglyregulargraphsfromquaternarycomplexhadamardmatrices |