Tree (saddle)

A tree (saddle) in mathematical graph theory is a special type of subset within a graph—a structure made up of points (vertices) and connecting lines (edges). It consists of two parts: a spanning tree, which connects all points without cycles, and an additional edge (the "saddle") that, when added, creates exactly one cycle. This concept helps analyze network properties and optimize routes, often used in areas like network design and circuit analysis. Essentially, a tree (saddle) balances connected simplicity with a minimal added link to introduce a controlled cycle.