Luo, Zuojuan; Zhou, Bo Nodal domain count and vertex bipartiteness. (English) Zbl 1488.05193 Ars Comb. 141, 369-374 (2018). 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 \(\nu_G=4\). Cited in 1 Document MSC: 05C15 Coloring of graphs and hypergraphs 05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) Keywords:nodal domain count; vertex bipartiteness; independent number; diameter; chromatic number PDFBibTeX XMLCite \textit{Z. Luo} and \textit{B. Zhou}, Ars Comb. 141, 369--374 (2018; Zbl 1488.05193)