Isomorphism of circulant graphs and digraphs
Brian Alspach,T. D. Parsons +1 more
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This paper proves the conjecture true if n = pq where p and q are distinct primes true, and shows that the conjecture is false in most cases when n is divisible by p2 where p is an odd prime, or n isdivisible by 24.About:
This article is published in Discrete Mathematics.The article was published on 1979-02-01 and is currently open access. It has received 132 citations till now. The article focuses on the topics: Circulant matrix & Circulant graph.read more
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Circulants and their connectivities
Frank Boesch,Ralph Tindell +1 more
TL;DR: A new result is presented which answers the previously unsolved question of characterizing the connection sequence of circulants having point connectivity equal to point degree and develops some theorems regarding a new generalization of connectivity known as super-connectivity.
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On isomorphisms of finite Cayley graphs: a survey
TL;DR: This article is devoted to surveying results, open problems and methods in the study of the isomorphism problem for Cayley graphs.
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Isomorphism problem for relational structures with a cyclic automorphism
TL;DR: It is proved that the isomorphism classes of all n -element relational structures (not only graphs) with cyclic automorphism have the anticipated simple form if and only if n = 1 or n = 4, where ϕ( n ) is Euler's ϕ function.
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A Solution of the Isomorphism Problem for Circulant Graphs
TL;DR: The isomorphism problem for Cayley graphs over the cyclic group has been solved in this article, and the main result of this paper is that the Cayley graph is a Cayley cyclic graph.
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Finite Transitive Permutation Groups and Bipartite Vertex-Transitive Graphs
TL;DR: The theory of vertex-transitive graphs has developed in parallel with the theory of transitive permutation groups as mentioned in this paper, and the authors in this paper explore the way the two theories have influenced each other.
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Graphs with circulant adjacency matrices
Bernard Elspas,James Turner +1 more
TL;DR: In this paper, the connection set determined by the first row of a circulant adjacency matrix is shown to not be multiplicatively related to the connected set of an isomorphic graph.
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Point-symmetric graphs with a prime number of points
TL;DR: In this article, the eigenvalues of the adjacency matrices of point-symmetric graphs with a prime number of points are characterized and group-graphs are defined.