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Nodal domain count and vertex bipartiteness. (English) Zbl 1488.05193

Summary: We establish a 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 of the independent number, and the diameter, and the chromatic number, and characterize the (connected) graphs \(G\) with \(\nu_G=4\).

MSC:

05C15 Coloring of graphs and hypergraphs
05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)
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