منابع مشابه
Which Haar graphs are Cayley graphs?
For a finite group G and subset S of G, the Haar graph H(G,S) is a bipartite regular graph, defined as a regular G-cover of a dipole with |S| parallel arcs labelled by elements of S. If G is an abelian group, then H(G,S) is well-known to be a Cayley graph; however, there are examples of non-abelian groups G and subsets S when this is not the case. In this paper we address the problem of classif...
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In a recent paper (arXiv:1505.01475 ) Estélyi and Pisanski raised a question whether there exist vertex-transitive Haar graphs that are not Cayley graphs. In this note we construct an infinite family of trivalent Haar graphs that are vertex-transitive but non-Cayley. The smallest example has 40 vertices and is the well-known Kronecker cover over the dodecahedron graph G(10, 2), occurring as the...
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Let G be a non-trivial group, S ⊆ G \ {1} and S = S−1 := {s−1 | s ∈ S}. The Cayley graph of G denoted by Γ(S : G) is a graph with vertex set G and two vertices a and b are adjacent if ab−1 ∈ S. A graph is called integral, if its adjacency eigenvalues are integers. In this paper we determine all connected cubic integral Cayley graphs. We also introduce some infinite families of connected integra...
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The original aim of this paper is to construct a graph associated to a vector space. By inspiration of the classical definition for the Cayley graph related to a group we define Cayley graph of a vector space. The vector space Cayley graph ${rm Cay(mathcal{V},S)}$ is a graph with the vertex set the whole vectors of the vector space $mathcal{V}$ and two vectors $v_1,v_2$ join by an edge whenever...
متن کاملOn the Problem of Determining which (n, k)-Star Graphs are Cayley Graphs
In this paper we work to classify which of the (n, k)-star graphs, denoted by Sn,k, are Cayley graphs. Although the complete classification is left open, we derive infinite and non-trivial classes of both Cayley and non-Cayley graphs. We give a complete classification of the case when k = 2, showing that Sn,2 is Cayley if and only if n is a prime power. Additionally, it is shown that Sn,n−2 is ...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2016
ISSN: 1077-8926
DOI: 10.37236/5240