The log concavity of two graphical sequences
Combinatorics
2025-01-22 v2 Cryptography and Security
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.
Keywords
Cite
@article{arxiv.2501.03709,
title = {The log concavity of two graphical sequences},
author = {Minjia Shi and Lu Wang and Patrick Sole},
journal= {arXiv preprint arXiv:2501.03709},
year = {2025}
}