Topological graph dimension
type: Item
instance of: scholarly article
title: Topological graph dimension
zbMATH Open document ID: 1191.05035
author: B. E. Eshmatov
published in: Discrete Mathematics
publication date: 2010-03-29T00:00:00Z
review text: 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.
reviewed by: Arthur T. White
Mathematics Subject Classification ID: 05C10
zbMATH DE Number: 5687561
zbMATH Keywords: graph dimension
zbMATH Keywords: small inductive dimension
zbMATH Keywords: planar graphs
MaRDI profile type: Publication
full work available at URL: j.disc.2008.10.003
OpenAlex ID: W2072734279
cites work: Dimension on discrete spaces
cites work: Topological properties of the intersection graph of covers of \(n\)-dimensional surfaces
cites work: Dimensional properties of graphs and digital spaces.
cites work: Planar graphs and poset dimension
cites work: Special issue: Spatial representation: Discrete vs. continuous computational models. Papers of the workshop, Schloss Dagstuhl, Germany, August 2004.
DOI: 10.1016/J.DISC.2008.10.003
description: scientific article; zbMATH DE number 5687561