Quasi-Spectral Characterization of Strongly Distance-Regular Graphs
نویسندگان
چکیده
منابع مشابه
Quasi-Spectral Characterization of Strongly Distance-Regular Graphs
A graph Γ with diameter d is strongly distance-regular if Γ is distanceregular and its distance-d graph Γd is strongly regular. The known examples are all the connected strongly regular graphs (i.e. d = 2), all the antipodal distanceregular graphs, and some distance-regular graphs with diameter d = 3. The main result in this paper is a characterization of these graphs (among regular graphs with...
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This is a new contribution to the question: Can we see from the spectrum of a graph whether it is distance-regular? By generalizing some results of Van Dam and Haemers, among others, we give some new spectral and quasi-spectral characterizations of distance-regularity. In this area of research, typical results concluding that a graph is distance regular require that G is cospectral with a dista...
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In [3] Cameron et al. classified strongly regular graphs with strongly regular subconstituents. Here we prove a theorem which implies that distance-regular graphs with strongly regular subconstituents are precisely the Taylor graphs and graphs with a1 = 0 and ai ∈ {0, 1} for i = 2, . . . , d .
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When can one see from the spectrum of a graph whether it is distance-regular or not? We give some new results for when this is the case. As a consequence we find (among others) that the following distance-regular graphs are uniquely determined by their spectrum: The collinearity graphs of the generalized octagons of order (2, 1), (3, 1) and (4, 1), the Biggs-Smith graph, the M22 graph, and the ...
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Article history: Received 9 April 2013 Accepted 15 December 2013 Available online 13 January 2014 Submitted by R. Brualdi
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2000
ISSN: 1077-8926
DOI: 10.37236/1529