A Construction of a Smooth Travel Groupoid on a Spanning Tree Associated with Lotus Graphs

Husnul Khotimah, Andi Tenri Ajeng Nur, Putri Nilam Cayo

Abstract


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 \leq i \leq 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.

Keywords


Travel Groupoid; Smooth Travel Groupoid; Lotus Graph; Spanning Tree; Binary Operation

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DOI: https://doi.org/10.37905/jjom.v8i2.38029

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