bibkey: phamvu2026wellcoveredpowers
authors: My Hanh Pham, Thanh Vu
year: 2026
title: "On graphs whose powers are well-covered"
doi: null
url: https://arxiv.org/abs/2610.09300v1
claim: "Positive graph powers use bounded path length; well-coveredness means equality of maximal independent-set cardinalities."
strata_touched:
  - D5/S3/Combinatorics/Graph/Products/CayleyCharacterization
license: citation-only
triage: anchor

Well-covered positive graph powers

Verified locator

https://arxiv.org/abs/2610.09300v1

The introduction and Definitions 2.2–2.3 define graph powers by paths of length at most the positive exponent and the property that all such powers are well-covered. Distinct components remain nonadjacent. Well-coveredness can equivalently be expressed by equal cardinalities of inclusion-maximal independent sets, using complementation between independent sets and vertex covers.

This reference supplies the terminology and power convention. The abelian Cayley square characterization and the deleted-vertex layer construction are separate mathematical arguments; they are not attributed to this paper.