192,037 research outputs found
Construction of cycle double covers for certain classes of graphs
We introduce two classes of graphs, Indonesian graphs and -doughnut graphs. Cycle double covers are constructed for these classes. In case of doughnut graphs this is done for the values and 4
Generalised morphisms of k-graphs: k-morphs
In a number of recent papers, (k+l)-graphs have been constructed from
k-graphs by inserting new edges in the last l dimensions. These constructions
have been motivated by C*-algebraic considerations, so they have not been
treated systematically at the level of higher-rank graphs themselves. Here we
introduce k-morphs, which provide a systematic unifying framework for these
various constructions. We think of k-morphs as the analogue, at the level of
k-graphs, of C*-correspondences between C*-algebras. To make this analogy
explicit, we introduce a category whose objects are k-graphs and whose
morphisms are isomorphism classes of k-morphs. We show how to extend the
assignment \Lambda \mapsto C*(\Lambda) to a functor from this category to the
category whose objects are C*-algebras and whose morphisms are isomorphism
classes of C*-correspondences.Comment: 27 pages, four pictures drawn with Tikz. Version 2: title changed and
numerous minor corrections and improvements. This version to appear in Trans.
Amer. Math. So
Expanding graphs, Ramanujan graphs, and 1-factor perturbations
We construct (k+-1)-regular graphs which provide sequences of expanders by
adding or substracting appropriate 1-factors from given sequences of k-regular
graphs. We compute numerical examples in a few cases for which the given
sequences are from the work of Lubotzky, Phillips, and Sarnak (with k-1 the
order of a finite field). If k+1 = 7, our construction results in a sequence of
7-regular expanders with all spectral gaps at least about 1.52
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