Topological graph dimension
Inspired by \textit{A. V. Evako}, \textit{R. Kopperman} and \textit{Y. V. Mukhin} [J. Math. Imaging Vision 6, 109--119 (1996; Zbl 1191.05088)], the authors introduce a concept of dimension for graphs which has two distinctive features: {\parindent=7mm \begin{itemize}\item[(1)]dimension at a vertex is basic, and the dimension of a graph is obtained as the supremum over its vertices; \item[(2)]\(\dim(G\times H)= \dim(G)+ \dim(H)\), where \(G\) and \(H\) are both nonempty graphs and ``\(\times\)'' denotes what the authors call ``a strong product''. \end{itemize}} They present a short account of the basic theory, with several new results and applications.
scientific article; zbMATH DE number 5687561