Minimum degree, edge-connectivity and radius

Baoyindureng Wu (), Xinhui An, Guojie Liu, Guiying Yan and Xiaoping Liu
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Baoyindureng Wu: Xinjiang University
Xinhui An: Xinjiang University
Guojie Liu: Xinjiang University
Guiying Yan: Chinese Academy of Sciences
Xiaoping Liu: Xinjiang Polytechnical College

Journal of Combinatorial Optimization, 2013, vol. 26, issue 3, No 14, 585-591

Abstract: 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: (1) G is K 5, (2) G≅K n ∖M, where M is a perfect matching, if n is even, (3) 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, Vukičević, Aouchice, and Hansen.

Keywords: Edge-connectivity; Radius; Minimum degree (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10878-012-9479-6

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