An Interesting Property of a Class of Circulant Graphs
Suppose that Π=Cay(Zn,Ω) and Λ=Cay(Zn,Ψm) are two Cayley graphs on the cyclic additive group Zn, where n is an even integer, m=n/2+1, Ω=t∈Zn∣t is odd, and Ψm=Ω∪{n/2} are the inverse-closed subsets of Zn-0. In this paper, it is shown that Π is a distance-transitive graph, and, by this fact, we dete...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2017-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2017/6454736 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | Suppose that Π=Cay(Zn,Ω) and Λ=Cay(Zn,Ψm) are two Cayley graphs on the cyclic additive group Zn, where n is an even integer, m=n/2+1, Ω=t∈Zn∣t is odd, and Ψm=Ω∪{n/2} are the inverse-closed subsets of Zn-0. In this paper, it is shown that Π is a distance-transitive graph, and, by this fact, we determine the adjacency matrix spectrum of Π. Finally, we show that if n≥8 and n/2 is an even integer, then the adjacency matrix spectrum of Λ is n/2+11, 1-n/21, 1n-4/2, -1n/2 (we write multiplicities as exponents). |
|---|---|
| ISSN: | 2314-4629 2314-4785 |