A family of graphs whose independence polynomials are both palindromic and unimodal

Vadim E. Levit, Eugen Mandrescu

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

a stable (or independent) set in a graph is a set of pairwise non-adjacent vertices. The stability number α(G) is the size of a maximum stable set in the graph G. The independence polynomial of G is defined by I(G; x) = s 0 + s1x + s2x2 + ... + s αxα, α = α(G), where sk equals the number of stable sets of cardinality k in G (I. Gutman and F. Harary 1983). In this paper, we build a family of graphs whose independence polynomials are palindromic and unimodal. We conjecture that all these polynomials are also log-concave.

Original languageEnglish
Pages (from-to)108-116
Number of pages9
JournalCarpathian Journal of Mathematics
Volume23
Issue number1-2
StatePublished - 2007

Keywords

  • Clique-cover
  • Independence polynomial
  • Palindromic polynomial
  • Real roots
  • Stable set
  • Uni-modality

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