23,135 research outputs found
Distance-regular graphs
This is a survey of distance-regular graphs. We present an introduction to
distance-regular graphs for the reader who is unfamiliar with the subject, and
then give an overview of some developments in the area of distance-regular
graphs since the monograph 'BCN' [Brouwer, A.E., Cohen, A.M., Neumaier, A.,
Distance-Regular Graphs, Springer-Verlag, Berlin, 1989] was written.Comment: 156 page
Cataloguing PL 4-manifolds by gem-complexity
We describe an algorithm to subdivide automatically a given set of PL
n-manifolds (via coloured triangulations or, equivalently, via
crystallizations) into classes whose elements are PL-homeomorphic. The
algorithm, implemented in the case n=4, succeeds to solve completely the
PL-homeomorphism problem among the catalogue of all closed connected PL
4-manifolds up to gem-complexity 8 (i.e., which admit a coloured triangulation
with at most 18 4-simplices). Possible interactions with the (not completely
known) relationship among different classification in TOP and DIFF=PL
categories are also investigated. As a first consequence of the above PL
classification, the non-existence of exotic PL 4-manifolds up to gem-complexity
8 is proved. Further applications of the tool are described, related to
possible PL-recognition of different triangulations of the K3-surface.Comment: 25 pages, 5 figures. Improvements suggested by the refere
Graph ambiguity
In this paper, we propose a rigorous way to define the concept of ambiguity in the domain of graphs. In past studies, the classical definition of ambiguity has been derived starting from fuzzy set and fuzzy information theories. Our aim is to show that also in the domain of the graphs it is possible to derive a formulation able to capture the same semantic and mathematical concept. To strengthen the theoretical results, we discuss the application of the graph ambiguity concept to the graph classification setting, conceiving a new kind of inexact graph matching procedure. The results prove that the graph ambiguity concept is a characterizing and discriminative property of graphs. (C) 2013 Elsevier B.V. All rights reserved
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