Fonctions harmoniques sur les graphes. (Harmonic functions on graphs)
type: Item
instance of: scholarly article
title: Fonctions harmoniques sur les graphes. (Harmonic functions on graphs)
zbMATH Open document ID: 0595.31013
DOI: 10.1007/BF01189865
author: Ezzeddine Haouala
published in: Archiv der Mathematik
publication date: 1986-01-01T00:00:00Z
review text: Let G be a finite connected graph. A 2-edge-connected component C is extremal if \(G\setminus C\) is connected. In this paper we show that the maximum m(G) of the dimension of \({\mathcal H}(G)\), when (G,\({\mathcal H}^*)\) is a harmonic space, is determined by the space of flows \({\mathcal F}(G)\) and the number c(G) of extremal 2-edge-connected components of \(G: m(G)=\dim {\mathcal F}(G)+\max (1,c(G)-1).\)
Mathematics Subject Classification ID: 31B99
Mathematics Subject Classification ID: 05C35
Mathematics Subject Classification ID: 05C40
zbMATH DE Number: 3957588
zbMATH Keywords: finite connected graph
zbMATH Keywords: harmonic space
zbMATH Keywords: extremal 2-edge-connected components
zbMATH Keywords: maximal dimension
MaRDI profile type: Publication
cites work: Q4096964
cites work: Q5662251
cites work: Q5627008
cites work: Q4183848
full work available at URL: https://doi.org/10.1007/bf01189865
OpenAlex ID: W2046245462
description: scientific article; zbMATH DE number 3957588