English

Independence equivalence classes of paths

Combinatorics 2022-09-14 v4

Abstract

The independence equivalence class of a graph GG is the set of graphs that have the same independence polynomial as GG. A graph whose independence equivalence class contains only itself, up to isomorphism, is independence unique. Beaton, Brown and Cameron (2019) showed that paths with an odd number of vertices are independence unique and raised the problem of finding the independence equivalence class of paths with an even number of vertices. The problem is completely solved in this paper.

Keywords

Cite

@article{arxiv.2105.01592,
  title  = {Independence equivalence classes of paths},
  author = {Boon Leong Ng},
  journal= {arXiv preprint arXiv:2105.01592},
  year   = {2022}
}
R2 v1 2026-06-24T01:46:27.509Z