vol10_pp179-189. 162KB Jun 04 2011 12:05:50 AM
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what we have in fact showed is the weaker result that the above digraph is optimal among digraphs with k edges and m + 1 vertices..
Minimum rank, Symmetric matrix, Finite field, Projective geometry, Polarity graph, Bilinear symmetric form. AMS
It was later extended to regular rings by Guralnick [6], who showed that over a regular ring, Roth’s equivalence property holds if and only if R is stably finite.. In a parallel
Then every column of B corresponding to e or its parallel arcs is the zero vector, and the submatrix consisting of the remaining columns of B is the incidence matrix of the digraph D
Theorem 1.2. Proof of Theorem 1.1. We will use the following auxiliary results in the proof.. Let SvwT denote the graph obtained from disjoint graphs S, T by adding an edge joining
Although deleting old edges in the uniformly grown graph changes abruptly the properties of the model, we show that some of the macro-characteristics of the graph vary continuously..
If M has a factor graph which is almost surely a locally finite one-ended tree then it has a factor graph which is almost surely a directed doubly infinite
We will prove that if a limit measure is not absolutely continuous with respect to the Lebesgue measure then the corresponding random walk on the self similar graph does not have
