منابع مشابه
Cyclic Haar graphs
For a given group with a generating set A a dipole with jAj parallel directed edges labeled by elements of A gives rise to a voltage graph whose covering graph denoted by H A is a bipartite regular graph called a bi Cayley graph In the case when is abelian we refer to H A as a Haar graph of with respect to the symbol A In particular for cyclic the above graph is referred to as a cyclic Haar gra...
متن کاملWhich 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...
متن کاملVertex-transitive Haar graphs that are not Cayley graphs
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...
متن کاملUnsupervised Deep Haar Scattering on Graphs
The classification of high-dimensional data defined on graphs is particularly difficult when the graph geometry is unknown. We introduce a Haar scattering transform on graphs, which computes invariant signal descriptors. It is implemented with a deep cascade of additions, subtractions and absolute values, which iteratively compute orthogonal Haar wavelet transforms. Multiscale neighborhoods of ...
متن کاملCyclic Graphs
A subclass of the class of circulant graphs is considered. It is shown that in this subclass, isomorphism is equivalent to Adam-isomorphism. Various results are obtained for the chromatic number, line-transitivity and the diameter.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2002
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(01)00064-4