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}
}