A Construction of a Smooth Travel Groupoid on a Spanning Tree Associated with Lotus Graphs - Husnul Khotimah; Andi Tenri Ajeng Nur; Putri Nilam Cayo (Department of Mathematics, Universitas Negeri Gorontalo, 2025)
A travel groupoid is a binary system associated with a graph through an operation on its vertex set, while a smooth travel groupoid satisfies an additional smoothness condition. In this paper, we construct a smooth travel groupoid on a particular spanning tree associated with the lotus graph L(n). The spanning tree is obtained by deleting the edges u_i v_i+1, for 1 ≤ i ≤ n-1, from the lotus graph. Using the unique path between two vertices in this tree, we define a binary operation by assigning to each ordered pair the first step from one vertex toward the other. We prove that the resulting binary system satisfies the axioms of a travel groupoid and fulfills the smoothness condition. Explicit examples for L(2) and L(3) are also presented to illustrate the construction.