%0 Journal Article %1 dalfo12 %A Dalfó, C. %A van Dam, E.R. %A Fiol, Miquel Àngel %A Garriga, E. %D 2012 %J Discrete Mathematics %K distance-regular eigenvalues graph.theory polynomial predistance spectral.graph.theory %N 17 %P 2730 -- 2734 %R j.disc.2012.03.003 %T Dual Concepts of Almost Distance-Regularity and the Spectral Excess Theorem %V 312 %X Generally speaking, ‘almost distance-regular’ graphs share some, but not necessarily all, of the regularity properties that characterize distance-regular graphs. In this paper we propose two new dual concepts of almost distance-regularity, thus giving a better understanding of the properties of distance-regular graphs. More precisely, we characterize m -partially distance-regular graphs and j -punctually eigenspace distance-regular graphs by using their spectra. Our results can also be seen as a generalization of the so-called spectral excess theorem for distance-regular graphs, and they lead to a dual version of it.

@article{dalfo12, abstract = {Generally speaking, ‘almost distance-regular’ graphs share some, but not necessarily all, of the regularity properties that characterize distance-regular graphs. In this paper we propose two new dual concepts of almost distance-regularity, thus giving a better understanding of the properties of distance-regular graphs. More precisely, we characterize m -partially distance-regular graphs and j -punctually eigenspace distance-regular graphs by using their spectra. Our results can also be seen as a generalization of the so-called spectral excess theorem for distance-regular graphs, and they lead to a dual version of it. }, added-at = {2015-08-13T13:16:48.000+0200}, author = {Dalfó, C. and van Dam, E.R. and Fiol, Miquel \`{A}ngel and Garriga, E.}, biburl = {https://www.bibsonomy.org/bibtex/2066a1d43208b4715becd3db9637ecb76/ytyoun}, doi = {j.disc.2012.03.003}, interhash = {8b8b8871e7f573ef845c23bb82af4826}, intrahash = {066a1d43208b4715becd3db9637ecb76}, issn = {0012-365X}, journal = {Discrete Mathematics }, keywords = {distance-regular eigenvalues graph.theory polynomial predistance spectral.graph.theory}, note = {Proceedings of the 8th French Combinatorial Conference }, number = 17, pages = {2730 -- 2734}, timestamp = {2016-11-16T08:08:03.000+0100}, title = {Dual Concepts of Almost Distance-Regularity and the Spectral Excess Theorem }, volume = 312, year = 2012 }