2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/146001In this paper necessary and sufficient conditions are presented for heat kernel upper bounds for random walks on weighted graphs. Several equivalent conditions are given in the form of isoperimetric inequalities.graphics are not includedProbability60J10; 60J45; 62M15Upper bounds for transition probabilities on graphs and isoperimetric inequalitiestext