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.
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