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Minimum degree, edge-connectivity and radius

Authors:	Baoyindureng Wu Xinhui An Guojie Liu Guiying Yan Xiaoping Liu

Institution:	1. College of Mathematics and System Science, Xinjiang University, Urumqi, Xinjiang, 830046, P.R. China 2. Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing, 100080, P.R. China 3. Xinjiang Polytechnical College, Urumqi, Xinjiang, 830000, P.R. China

Abstract:	Let G be a connected graph on n≥4 vertices with minimum degree δ and radius r. Then $\delta r\leq4\lfloor\frac{n}{2}\rfloor-4$ , with equality if and only if one of the following holds: G is K ₅, G?K _n?M, where M is a perfect matching, if n is even, δ=n?3 and Δ≤n?2, if n is odd. This solves a conjecture on the product of the edge-connectivity and radius of a graph, which was posed by Sedlar, Vuki?evi?, Aouchice, and Hansen.

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