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...
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| Format: | Article |
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Wiley
2017-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2017/6454736 |
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| author | Seyed Morteza Mirafzal Ali Zafari |
| author_facet | Seyed Morteza Mirafzal Ali Zafari |
| author_sort | Seyed Morteza Mirafzal |
| collection | DOAJ |
| description | 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). |
| format | Article |
| id | doaj-art-f686a8bf9a054c52b60617b40684dc5b |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-f686a8bf9a054c52b60617b40684dc5b2025-02-03T05:49:57ZengWileyJournal of Mathematics2314-46292314-47852017-01-01201710.1155/2017/64547366454736An Interesting Property of a Class of Circulant GraphsSeyed Morteza Mirafzal0Ali Zafari1Department of Mathematics, Lorestan University, Khoramabad, IranDepartment of Mathematics, Lorestan University, Khoramabad, IranSuppose 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).http://dx.doi.org/10.1155/2017/6454736 |
| spellingShingle | Seyed Morteza Mirafzal Ali Zafari An Interesting Property of a Class of Circulant Graphs Journal of Mathematics |
| title | An Interesting Property of a Class of Circulant Graphs |
| title_full | An Interesting Property of a Class of Circulant Graphs |
| title_fullStr | An Interesting Property of a Class of Circulant Graphs |
| title_full_unstemmed | An Interesting Property of a Class of Circulant Graphs |
| title_short | An Interesting Property of a Class of Circulant Graphs |
| title_sort | interesting property of a class of circulant graphs |
| url | http://dx.doi.org/10.1155/2017/6454736 |
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