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arXiv · 2501.03709

The log concavity of two graphical sequences

Minjia Shi·Lu Wang·Patrick Sole
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Abstract

We show that the large Cartesian powers of any graph have log-concave valencies with respect to a ffxed vertex. We show that the series of valencies of distance regular graphs is log-concave, thus improving on a result of (Taylor, Levingston, 1978). Consequences for strongly regular graphs, two-weight codes, and completely regular codes are derived. By P-Q duality of association schemes the series of multiplicities of Q-polynomial association schemes is shown, under some assumption, to be log-concave.

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Minjia Shi, Lu Wang, Patrick Sole. 2025-01-20. The log concavity of two graphical sequences. https://arxiv.org/abs/2501.03709

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