English

Complete r-partite graphs determined by their domination polynomial

Combinatorics 2013-04-03 v2

Abstract

The domination polynomial of a graph is the polynomial whose coefficients count the number of dominating sets of each cardinality. A recent question asks which graphs are uniquely determined (up to isomorphism) by their domination polynomial. In this paper, we completely describe the complete r-partite graphs which are; in the bipartite case, this settles in the affirmative a conjecture of Aalipour, Akbari and Ebrahimi.

Keywords

Cite

@article{arxiv.1303.5999,
  title  = {Complete r-partite graphs determined by their domination polynomial},
  author = {Barbara M. Anthony and Michael E. Picollelli},
  journal= {arXiv preprint arXiv:1303.5999},
  year   = {2013}
}

Comments

13 pages, 3 figures - corrected references, adjusted start of Section 2

R2 v1 2026-06-21T23:47:25.671Z