On 3-isoregularity of multicirculants
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915129372704768 |
|---|---|
| author | Kutnar, Klavdija Marušič, Dragan Miklavič, Štefko |
| author_facet | Kutnar, Klavdija Marušič, Dragan Miklavič, Štefko |
| contents | A graph is said to be $k$-{\em isoregular} if any two vertex subsets of cardinality at most $k$, that induce subgraphs of the same isomorphism type, have the same number of neighbors. It is shown that no $3$-isoregular bicirculant (and more generally, no locally $3$-isoregular bicirculant) of order twice an odd number exists. Further, partial results for bicirculants of order twice an even number as well as tricirculants of specific orders, are also obtained. Since $3$-isoregular graphs are necessarily strongly regular, the above result about bicirculants, among other, brings us a step closer to obtaining a direct proof of a classical consequence of the Classification of Finite Simple Groups that no simply primitive group of degree twice a prime exists for primes greater than $5$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18217 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On 3-isoregularity of multicirculants Kutnar, Klavdija Marušič, Dragan Miklavič, Štefko Combinatorics 05E18 A graph is said to be $k$-{\em isoregular} if any two vertex subsets of cardinality at most $k$, that induce subgraphs of the same isomorphism type, have the same number of neighbors. It is shown that no $3$-isoregular bicirculant (and more generally, no locally $3$-isoregular bicirculant) of order twice an odd number exists. Further, partial results for bicirculants of order twice an even number as well as tricirculants of specific orders, are also obtained. Since $3$-isoregular graphs are necessarily strongly regular, the above result about bicirculants, among other, brings us a step closer to obtaining a direct proof of a classical consequence of the Classification of Finite Simple Groups that no simply primitive group of degree twice a prime exists for primes greater than $5$. |
| title | On 3-isoregularity of multicirculants |
| topic | Combinatorics 05E18 |
| url | https://arxiv.org/abs/2501.18217 |