On Jacobian group of the $\Delta$-graph

TL;DR

This paper computes the Jacobian group of a family of $ riangle$-graphs, extending known graph families, and explicitly determines the structure for a specific case related to the discrete torus.

Contribution

It introduces the $ riangle$-graph family and provides explicit computation of their Jacobian groups, including the case of the discrete torus $C_3 imes C_n$.

Findings

Explicit Jacobian group structure for $ riangle(n; 1, 1, 1)$

Extension of known graph families to $ riangle$-graphs

New formulas for Jacobian groups of $ riangle$-graphs

Abstract

In the present paper we compute the Jacobian group of $\Delta$-graph $\Delta(n; k, l, m).$ The notion of $\Delta$-graph continues the list of families of $I$-, $Y$- and $H$-graphs well-known in the graph theory. In particular, graph $\Delta(n; 1, 1, 1)$ is isomorphic to discrete torus $C_3\times C_n.$ It this case, the structure of the Jacobian group will be find explicitly.