»ã±¨±êÌâ (Title)£ºCurvature and local matchings of amply regular graphs (amply regularͼµÄÇúÂʺͲ¿ÃÅͼµÄÆ¥Åä)

»ã±¨ÈË (Speaker)£ºÁõÊÀƽ ½ÌÊÚ£¨Öйú¿Æѧ¼¼Êõ´óѧ£©

»ã±¨¹¦·ò (Time)£º2024Äê9ÔÂ13ÈÕ(ÖÜÎå) 10:00

»ã±¨µØÖ· (Place)£ºÌÚѶ»áÒé 271-962-145

Ô¼ÇëÈË(Inviter)£ºÑîٻٻ

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»ã±¨ÌáÒª£º Bounding the diameter of a distance-regular graph in terms of its intersection numbers is a very important problem. Recently, there are strong interests to bound the diameter via a small initial part of the intersection array (see, e.g., Neumaier-Penji?, Combinatorica 2022). For that purpose, we consider the diameter estimates of a more general class of graphs called amply regular graphs. In differential geometry, a general principle is that the curvature lower bounds at every point of a space leads to a diameter upper bound. In this talk, we will discuss sharp diameter bounds for amply regular graphs derived from estimating the Lin-Lu-Yau curvature of each edge. Calculating the Lin-Lu-Yau curvature often reduces to showing the existence of certain local matching conditions. We will further address a conjecture of Bonini et. al. in 2020 on the curvature of conference graphs. This talk is based on joint works with Xueping Huang, Qing Xia, Kaizhe Chen, and Heng Zhang.