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 rr-partite graphs which are; in the bipartite case, this settles in the affirmative a conjecture of Aalipour et al. (Ars Comb, 2014).
Description:
This is an Accepted Manuscript of an article published by Springer in Graphs and Combinatorics, 2015, 31(6), 1993–2002. http://doi.org/10.1007/s00373-014-1521-2
