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arXiv · 1207.3606

Dual concepts of almost distance-regularity and the spectral excess theorem

Cristina Dalfó·Edwin R. van Dam·Miquel Angel Fiol·Ernest Garriga
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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.

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Cristina Dalfó, Edwin R. van Dam, Miquel Angel Fiol, Ernest Garriga. 2012-07-16. Dual concepts of almost distance-regularity and the spectral excess theorem. https://doi.org/10.1016/j.disc.2012.03.003

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