Graphs and Digraphs: A graph G = (V,E) is a structure that represents a discrete set V objects, called vertices or nodes, and a set of pairwise relations E between these objects, called edges. Edges may be directed from one vertex to another or may be undirected. The term “graph” means an undirected graph, and directed graphs are often called digraphs (see Fig. 1). Graphs and digraphs provide a...

‎‎in the category of mordell curves (e_d:y^2=x^3+d) with nontrivial torsion groups we find curves of the generic rank two as quadratic twists of (e_1), ‎and of the generic rank at least two and at least three as cubic twists of (e_1). ‎previous work‎, ‎in the category of mordell curves with trivial torsion groups‎, ‎has found infinitely many elliptic curves with rank at least seven as sextic tw...