On certain arithmetic graphs and their applications to diophantine problems (Q1038646)

This is a continuation of the author's investigations [Publ. Math. 27, 229--242 (1980; Zbl 0466.05047), Publ. Math. 29, 79--94 (1982; Zbl 0522.10013), A tribute to Paul Erdős, 207--222 (1990; Zbl 0727.11039), Sets, graphs and numbers. Colloq. Math. Soc. János Bolyai 60, 365--374 (1992; Zbl 0798.11042)] on arithmetic graphs. Some general quantitative results are formulated for these graphs over finitely generated integral domains. The results have several applications to diophantine problems. Consequences on resultant equations and discriminant equations are formulated.