Overlap matrices and total imbedding distributions
type: Item
instance of: scholarly article
title: Overlap matrices and total imbedding distributions
zbMATH Open document ID: 0798.05017
DOI: 10.1016/0012-365X(94)90105-8
author: Jonathan L. Gross
author: Robert G. Rieper
author: Jianer Chen
published in: Discrete Mathematics
publication date: 1994-05-05T00:00:00Z
review text: For a given graph \(G\), let \(\alpha_ g(G)\), \(g= 0,1,2,\dots\), denote the number of homeomorphically different 2-cell embeddings of \(G\) in a surface of genus \(g\). The sequence \(\alpha_ g(G)\), \(g=0,1,2,\dots\), is the genus distribution of \(G\). This concept can be extended to include nonorientable embeddings. The authors determine the extended embedding distributions for several classes of graphs. The computations in the nonorientable case are done by applying a theorem of the reviewer [An obstruction to embedding graphs in surfaces, Discrete Math. 78, No. 1/2, 135-142 (1989; Zbl 0686.05019)] that relates the topological types of embedding surfaces to ranks of the corresponding overlap matrices.
Mathematics Subject Classification ID: 05C10
Mathematics Subject Classification ID: 05C50
zbMATH DE Number: 562584
zbMATH Keywords: genus distribution
zbMATH Keywords: embedding distributions
zbMATH Keywords: embedding surfaces
zbMATH Keywords: overlap matrices
reviewed by: Bojan Mohar
MaRDI profile type: Publication
cites work: Q3992537
cites work: Limit points for average genus. I: 3-connected and 2-connected simplicial graphs
cites work: Limit points for average genus. II: 2-connected non-simplicial graphs
cites work: Kuratowski-type theorems for average genus
cites work: On the surface duality of linear graphs
cites work: Genus distributions for two classes of graphs
cites work: Hierarchy for imbedding-distribution invariants of a graph
cites work: On the average genus of a graph
cites work: Genus distributions for bouquets of circles
cites work: Q3757929
cites work: Q3496299
cites work: An obstruction to embedding graphs in surfaces
cites work: Q4156452
cites work: How to determine the maximum genus of a graph
Wikidata QID: Q126297073
description: scientific article; zbMATH DE number 562584