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Spanning Trees in Directed Square Cycles by Tanaka, Yuuho is a scholarly article available to read on EtoBox.

What is Spanning Trees in Directed Square Cycles about?

We classify weakly connected spanning closed (WCSC) subgraphs of $\overrightarrow{C_n^2}$, the square of a directed $n$-vertex cycle. Then we show that every spanning tree of $\overrightarrow{C_n^2}$ is contained in a unique nontrivial WCSC subgraph of $\overrightarrow{C_n^2}$. As a result, we obtain a purely combinatorial derivation of the formula for the number of directed spanning trees of $\overrightarrow{C_n^2}$. Moreover, we obtain the formula for the number of directed spanning trees of $\overrightarrow{C_n^2}$, which is a Jacobsthal number.

Author

Tanaka, Yuuho

Published

2025

Language

EN