Spanning trees in directed square cycles

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

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Publication Details

Journal
Discrete Applied Mathematics
Published
2025-10-09
DOI
https://doi.org/10.1016/j.dam.2025.10.005
Primary Topic
Advanced Graph Theory Research
Type
article
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article

Spanning trees in directed square cycles

Yuuho Tanaka
Discrete Applied Mathematics
Advanced Graph Theory Research
article

Spanning trees in directed square cycles

Yuuho Tanaka
article en

Abstract

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

Discrete Applied MathematicsVol. 379
Oita University (JP)
Openalex Percentile: Top 70%
Advanced Graph Theory Research
DOIOpen Access PDFOpenAlex
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Spanning trees in directed square cycles — Yuuho Tanaka · Discrete Applied Mathematics (2025) | TGRS Research Map | TGRS