English

A matrix for counting paths in acyclic colored digraphs

Combinatorics 2024-04-04 v2

Abstract

In this paper, we introduce a matrix AΓk,RA_{\Gamma_{k, R}} associate with a kk-colored acyclic digraph Γk,R\Gamma_{k, R} such that det(AΓk,R)\text{det}(A_{\Gamma_{k, R}}) enumerates the paths in the digraph Γk,R.\Gamma_{k, R}.

Keywords

Cite

@article{arxiv.2204.03367,
  title  = {A matrix for counting paths in acyclic colored digraphs},
  author = {Sudip Bera},
  journal= {arXiv preprint arXiv:2204.03367},
  year   = {2024}
}

Comments

11 pages, 3 figures. Accepted manuscript for publication in Graphs and Combinatorics

R2 v1 2026-06-24T10:41:02.750Z