Nodal domain count and vertex bipartiteness

LUO Zuo-juan; ZHOU Bo

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Nodal domain count and vertex bipartiteness

LUO Zuo-juan, ZHOU Bo

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Funding: Specialized Research Fund for the Doctoral Program of HigherEducation of China （No.20124407110002）

Opened online: 4 December 2015

Accepted by: none

Citation: LUO Zuo-juan, ZHOU Bo.Nodal domain count and vertex bipartiteness[OL]. [ 4 December 2015] http://en.paper.edu.cn/en_releasepaper/content/4666784

We establish a novel relation between the nodal domain count and the vertex bipartiteness of a graph, give upper and/or lower bound for the nodal domain count of a graph in terms ofthe independent number, and the diameter, and the chromatic number, and characterize the (connected) graphs $G$ withnodal domain count $4$.

Keywords:nodal domain count, vertex bipartiteness, independent number, diameter, chromatic number

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