Guojie Liu

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Using Ore’s structural characterization on diameter-maximal graphs, we determine the extremal graphs with the minimum average distance among the graphs with given order and diameter, thereby solving a conjecture of Aouchiche and Hansen [Automated results and conjectures on average distance in graphs, in Graph Theory in Paris, eds. A. Bondy, J. Fonlupt,(More)
In this article, we introduce multiple vector-valued mutiresolution analysis and orthogonal multiple vector-valued wavelet packets. A method for constructing orthogonal multiple vector-valued wavelet packets is proposed. The orthogonality property of the multiple vector-valued wavelet packets has been investigated. Finally, a new orthogonal basis of(More)
Let G be a connected graph on n≥ 4 vertices with minimum degree δ and radius r . Then δr ≤ 4 n2 −4, with equality if and only if one of the following holds: (1) G is K5, (2) G∼=Kn \M , where M is a perfect matching, if n is even, (3) δ = n− 3 and ≤ n− 2, if n is odd. This solves a conjecture on the product of the edge-connectivity and radius of a graph,(More)
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