Dual concepts of almost distance-regularity and the spectral excess theorem
Document typeConference report
PublisherIniciativa Digital Politècnica
Rights accessOpen Access
Generally speaking, ‘almost distance-regular’ graphs are graphs that share some, but not necessarily all, regularity properties that characterize distance-regular graphs. In this paper we first propose two dual concepts of almost distance-regularity. In some cases, they coincide with concepts introduced before by other authors, such as partially distance-regular graphs. Our study focuses on finding out when almost distance-regularity leads to distance-regularity. In particular, some ‘economic’ (in the sense of minimizing the number of conditions) old and new characterizations of distance-regularity are discussed. Moreover, other characterizations based on the average intersection numbers and the recurrence coefficients are obtained. In some cases, our results can also be seen as a generalization of the so-called spectral excess theorem for distance-regular graphs.
CitationDalfó Simó, Cristina [et al.]. Dual concepts of almost distance-regularity and the spectral excess theorem. A: International Workshop on Optimal Networks Topologies. "Proceedings of the 3rd International Workshop on Optimal Networks Topologies IWONT 2010". Barcelona: Iniciativa Digital Politècnica, 2011, p. 209-226.
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder