The lower bound for number of hexagons in strongly regular graphs with parameters $\lambda=1$ and $\mu=2$
The existence of $srg(99,14,1,2)$ has been a question of interest for several decades to the moment. In this paper, we consider the structural properties in general for the family of strongly regular graphs with parameters $\lambda =1$ and $\mu =2$. In particular, we establish the lower bound for th...
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| Format: | Article |
| Language: | English |
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EJAAM
2024-08-01
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| Series: | E-Journal of Analysis and Applied Mathematics |
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| Online Access: | https://ejaam.org/articles/2024/10.62780-ejaam-2024-001.pdf |
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| author | Reimbay Reimbayev |
| author_facet | Reimbay Reimbayev |
| author_sort | Reimbay Reimbayev |
| collection | DOAJ |
| description | The existence of $srg(99,14,1,2)$ has been a question of interest for several decades to the moment. In this paper, we consider the structural properties in general for the family of strongly regular graphs with parameters $\lambda =1$ and $\mu =2$. In particular, we establish the lower bound for the number of hexagons, and by doing that, we show the connection between the existence of the aforementioned graph and the number of its hexagons. |
| format | Article |
| id | doaj-art-149de8e0f5af4371893ed32736bb5487 |
| institution | Kabale University |
| issn | 2544-9990 |
| language | English |
| publishDate | 2024-08-01 |
| publisher | EJAAM |
| record_format | Article |
| series | E-Journal of Analysis and Applied Mathematics |
| spelling | doaj-art-149de8e0f5af4371893ed32736bb54872025-02-08T18:35:22ZengEJAAME-Journal of Analysis and Applied Mathematics2544-99902024-08-01202410.62780/ejaam/2024-001The lower bound for number of hexagons in strongly regular graphs with parameters $\lambda=1$ and $\mu=2$Reimbay Reimbayev0Auburn University, Department of Mathematics and Statistics, Alabama, 36849, United States of AmericaThe existence of $srg(99,14,1,2)$ has been a question of interest for several decades to the moment. In this paper, we consider the structural properties in general for the family of strongly regular graphs with parameters $\lambda =1$ and $\mu =2$. In particular, we establish the lower bound for the number of hexagons, and by doing that, we show the connection between the existence of the aforementioned graph and the number of its hexagons.https://ejaam.org/articles/2024/10.62780-ejaam-2024-001.pdfstrongly regular graphexistence |
| spellingShingle | Reimbay Reimbayev The lower bound for number of hexagons in strongly regular graphs with parameters $\lambda=1$ and $\mu=2$ E-Journal of Analysis and Applied Mathematics strongly regular graph existence |
| title | The lower bound for number of hexagons in strongly regular graphs with parameters $\lambda=1$ and $\mu=2$ |
| title_full | The lower bound for number of hexagons in strongly regular graphs with parameters $\lambda=1$ and $\mu=2$ |
| title_fullStr | The lower bound for number of hexagons in strongly regular graphs with parameters $\lambda=1$ and $\mu=2$ |
| title_full_unstemmed | The lower bound for number of hexagons in strongly regular graphs with parameters $\lambda=1$ and $\mu=2$ |
| title_short | The lower bound for number of hexagons in strongly regular graphs with parameters $\lambda=1$ and $\mu=2$ |
| title_sort | lower bound for number of hexagons in strongly regular graphs with parameters lambda 1 and mu 2 |
| topic | strongly regular graph existence |
| url | https://ejaam.org/articles/2024/10.62780-ejaam-2024-001.pdf |
| work_keys_str_mv | AT reimbayreimbayev thelowerboundfornumberofhexagonsinstronglyregulargraphswithparameterslambda1andmu2 AT reimbayreimbayev lowerboundfornumberofhexagonsinstronglyregulargraphswithparameterslambda1andmu2 |