Graphs and Combinatorics

, Volume 31, Issue 6, pp 1993–2002 | Cite as

Complete \(r\)-partite Graphs Determined by their Domination Polynomial

Original Paper

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 et al. (Ars Comb, 2014).

Keywords

Domination polynomial Dominating set \(\mathcal{D}\)-unique graphs 

Mathematics Subject Classification

05C69 05C75 

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Copyright information

© Springer Japan 2015

Authors and Affiliations

  1. 1.Southwestern University1001 E. University AveGeorgetownUSA
  2. 2.California State University San MarcosSan MarcosUSA

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