Complete r-partite Graphs Determined by their Domination Polynomial
Item
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Title
Complete r-partite Graphs Determined by their Domination Polynomial
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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
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Creator
Anthony, Barbara M.
Picollelli, Michael E.
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Identifier
Anthony, B. M., & Picollelli, M. E. (2015). Complete r-partite Graphs Determined by their Domination Polynomial. Graphs and Combinatorics, 31(6), 1993–2002. http://doi.org/10.1007/s00373-014-1521-2
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uri
https://collections.southwestern.edu/s/suscholar/item/221
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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).
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Publisher
Springer http://link.springer.com/article/10.1007/s00373-014-1521-2
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Subject
Domination polynomial
Dominating set
DD -unique graphs
Research Subject Categories::MATHEMATICS
