On the spectrum of a class of distance-transitive graphs
Let $\Gamma=Cay(\mathbb{Z}_n, S_k)$ be the Cayley graph on the cyclic additive group $\mathbb{Z}_n$ $(n\geq 4),$ where $S_1=\{1, n-1\}$, \dots , $S_k=S_ {k-1}\cup\{k, n-k\}$ are the inverse-closed subsets of $\mathbb{Z}_n-\{0\}$ for any $k\in \mathbb{N}$, $1\leq k\leq [\frac{n}{2}]-1$. In this pap...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | EJournal Article |
| Published: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB,
2017-04-10.
|
| Subjects: | |
| Online Access: | Get Fulltext Get Fulltext |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| LEADER | 02131 am a22002773u 4500 | ||
|---|---|---|---|
| 001 | 0 nhttps:__www.ejgta.org_index.php_ejgta_article_downloadSuppFile_278_56 | ||
| 042 | |a dc | ||
| 100 | 1 | 0 | |a Mirafzal, Seyed Morteza; Department of Mathematics Lorestan University, Khoramabad, Iran |e author |
| 100 | 1 | 0 | |e contributor |
| 700 | 1 | 0 | |a Zafari, Ali; Department of Mathematics, Lorestan University, Khoramabad, Iran |e author |
| 245 | 0 | 0 | |a On the spectrum of a class of distance-transitive graphs |
| 260 | |b GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, |c 2017-04-10. | ||
| 500 | |a https://www.ejgta.org/index.php/ejgta/article/view/278 | ||
| 520 | |a Let $\Gamma=Cay(\mathbb{Z}_n, S_k)$ be the Cayley graph on the cyclic additive group $\mathbb{Z}_n$ $(n\geq 4),$ where $S_1=\{1, n-1\}$, \dots , $S_k=S_ {k-1}\cup\{k, n-k\}$ are the inverse-closed subsets of $\mathbb{Z}_n-\{0\}$ for any $k\in \mathbb{N}$, $1\leq k\leq [\frac{n}{2}]-1$. In this paper, we will show that $\chi(\Gamma) = \omega(\Gamma)=k+1$ if and only if $k+1|n$. Also, we will show that if $n$ is an even integer and $k=\frac{n}{2}-1$ then $Aut(\Gamma)\cong\mathbb{Z}_2 wr_{I} {Sym}(k+1)$ where $I=\{1, \dots , k+1\}$ and in this case, we show that $\Gamma$ is an integral graph. | ||
| 540 | |a Copyright (c) 2017 Electronic Journal of Graph Theory and Applications (EJGTA) | ||
| 546 | |a eng | ||
| 690 | |a Cayley graph, distance-transitive, wreath product | ||
| 655 | 7 | |a info:eu-repo/semantics/article |2 local | |
| 655 | 7 | |a info:eu-repo/semantics/publishedVersion |2 local | |
| 655 | 7 | |a Peer-reviewed Article |2 local | |
| 786 | 0 | |n Electronic Journal of Graph Theory and Applications (EJGTA); Vol 5, No 1 (2017): Electronic Journal of Graph Theory and Applications; 63-69 | |
| 786 | 0 | |n 2338-2287 | |
| 787 | 0 | |n https://www.ejgta.org/index.php/ejgta/article/view/278/pdf_37 | |
| 787 | 0 | |n https://www.ejgta.org/index.php/ejgta/article/downloadSuppFile/278/56 | |
| 856 | 4 | 1 | |u https://www.ejgta.org/index.php/ejgta/article/view/278/pdf_37 |z Get Fulltext |
| 856 | 4 | 1 | |u https://www.ejgta.org/index.php/ejgta/article/downloadSuppFile/278/56 |z Get Fulltext |