English

Enumerating simple paths from connected induced subgraphs

Combinatorics 2018-10-30 v2

Abstract

We present an exact formula for the ordinary generating series of the simple paths between any two vertices of a graph. Our formula involves the adjacency matrix of the connected induced subgraphs and remains valid on weighted and directed graphs. As a particular case, we obtain a relation linking the Hamiltonian paths and cycles of a graph to its dominating connected sets.

Keywords

Cite

@article{arxiv.1606.00289,
  title  = {Enumerating simple paths from connected induced subgraphs},
  author = {Pierre-Louis Giscard and Paul Rochet},
  journal= {arXiv preprint arXiv:1606.00289},
  year   = {2018}
}
R2 v1 2026-06-22T14:14:56.751Z