Fonctions harmoniques sur les graphes. (Harmonic functions on graphs) (Q1077593)

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 \(G: m(G)=\dim {\mathcal F}(G)+\max (1,c(G)-1).\)