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1.
On the isomorphisms and automorphism groups of circulants   总被引:2,自引:0,他引:2  
Denote byC n(S) the circulant graph (or digraph). LetM be a minimal generating element subset ofZ n, the cyclic group of integers modulon, and In this paper, we discuss the problems about the automorphism group and isomorphisms ofC n(S). When M S , we determine the automorphism group ofC n(S) and prove that for any T if and only ifT = S, where is an integer relatively prime ton. The automorphism groups and isomorphisms of some other types of circulant graphs (or digraphs) are also considered. In the last section of this paper, we give a relation between the isomorphisms and the automorphism groups of circulants.  相似文献
2.
Circulant digraphs determined by their spectra   总被引:1,自引:0,他引:1  
Inspired by Ádám's conjecture the isomorphism problem of circulant digraphs is widely investigated. In the literature, the spectrum method was to solve the isomorphism problem for the circulants of prime-power order by some people. In this paper, we develop the spectrum method to characterize the circulant digraphs of orders pa and paqb, where p and q are distinct primes.  相似文献
3.
对换网络和乘积循环网络的超连通性   总被引:1,自引:0,他引:1  
本文证明了对换网络和乘积循环网络是超连通的。  相似文献
4.
Laplacian spectral characterization of 3-rose graphs   总被引:1,自引:0,他引:1  
A 3-rose graph is a graph consisting of three cycles intersecting in a common vertex, J. Wang et al. showed all 3-rose graphs with at least one triangle are determined by their Laplacian spectra. In this paper, we complete the above Laplacian spectral characterization and prove that all 3-rose graphs are determined by their Laplacian spectra.  相似文献
5.
A note on the spectral characterization of dumbbell graphs   总被引:1,自引:0,他引:1  
The dumbbell graph, denoted by Da,b,c, is a bicyclic graph consisting of two vertex-disjoint cycles Ca and Cb joined by a path Pc+3 (c-1) having only its end-vertices in common with the two cycles. By using a new cospectral invariant for (r,r+1)-almost regular graphs, we will show that almost all dumbbell graphs (without cycle C4 as a subgraph) are determined by the adjacency spectrum.  相似文献
6.
Abstract. In this paper, we introduce a new approach to characterize the isomor-phisms of circulant digraphs. In terms of this method, we completely determine the isomorphic classes of circulant digraphs of degree 3. In psrticular, we characterize those circulant digraphs of degree 3 which don‘‘t satisfy JkdAm‘‘s conjectttre.  相似文献
7.
INFINITECIRCULANTSANDTHEIRPROPERTIESZHANGFUJI(张福基)HUANGQIONGXIANG(黄琼湘)(DepartmentofMathematics,XinjiangUniversity,Urumchi8300...  相似文献
8.
A multicone graph is defined to be the join of a clique and a regular graph. Based on Zhou and Cho’s result [B. Zhou, H.H. Cho, Remarks on spectral radius and Laplacian eigenvalues of a graph, Czech. Math. J. 55 (130) (2005), 781–790], the spectral characterization of multicone graphs is investigated. Particularly, we determine a necessary and sufficient condition for two multicone graphs to be cospectral graphs and investigate the structures of graphs cospectral to a multicone graph. Additionally, lower and upper bounds for the largest eigenvalue of a multicone graph are given.  相似文献
9.
A Π-shape tree is a tree with exactly two vertices having the maximum degree three. In this paper, we classify the Π-shape trees into two types, and complete the spectral characterization for one type. Exactly, we prove that all graphs of this type are determined by their Laplacian spectra with some exceptions. Moreover, we give some L-cospectral mates of some graphs for another type.  相似文献
10.
In this paper, we completely characterize the graphs with third largest distance eigenvalue at most \(-1\) and smallest distance eigenvalue at least \(-3\). In particular, we determine all graphs whose distance matrices have exactly two eigenvalues (counting multiplicity) different from \(-1\) and \(-3\). It turns out that such graphs consist of three infinite classes, and all of them are determined by their distance spectra. We also show that the friendship graph is determined by its distance spectrum.  相似文献
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