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Regular, pseudo-regular, and almost regular matrices
We give lower bounds on the largest singular value of arbitrary matrices, some of which are asymptotically tight for almost all matrices. To study when these bounds are exact, we introduce several combinatorial concepts. In particular, we introduce regular, pseudo-regular, and almost regular matrices. Nonnegative, symmetric, almost regular matrices were studied earlier by Ho¤man, Wolfe, and Ho¤...
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Suppose every vertex of a graph G has degree k or k + 1 and at least one vertex has degree k + 1. It is shown that if k > 2q 2 and q is a prime power then G contains a q-regular subgraph (and hence an r-regular subgraph for all r < q. r = q (mod 2)). It is also proved that every simple graph with maximal degree A > 2q 2 and average degree d > ((2q 2)/(2q l))(A + 1), where q is a prime power, co...
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Distance-regular graphs have been a key concept in Algebraic Combinatorics and have given place to several generalizations, such as association schemes. Motivated by spectral and other algebraic characterizations of distance-regular graphs, we study ‘almost distance-regular graphs’. We use this name informally for graphs that share some regularity properties that are related to distance in the ...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 1993
ISSN: 0035-7596
DOI: 10.1216/rmjm/1181072619