Spanning trees in directed circulant graphs and cycle power graphs

TL;DR

This paper evaluates the number of spanning trees in specific directed circulant graphs and cycle power graphs, providing explicit product formulas that depend on graph parameters.

Contribution

It introduces explicit product formulas for counting spanning trees in directed circulant graphs and cycle power graphs, extending previous combinatorial results.

Findings

Derived formulas for spanning trees in directed circulant graphs

Established product expressions for cycle power graphs

Extended combinatorial enumeration methods

Abstract

The number of spanning trees in a class of directed circulant graphs with generators depending linearly on the number of vertices $\beta n$, and in the $n$-th and $(n-1)$-th power graphs of the $\beta n$-cycle are evaluated as a product of $\lceil\beta/2\rceil-1$ terms.