On the independence polynomial of the corona of graphs

Vadim E. Levit, Eugen Mandrescu

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4 Scopus citations

Abstract

Let α(G) be the cardinality of a largest independent set in graph G. If sk is the number of independent sets of size k in G, then I(G;x)=s0+s1x+⋯+, α=α(G), is the independence polynomial of G (Gutman and Harary, 1983). I(G;x) is palindromic if sα-i=si for each iε{0,1,⋯,⌊α/2⌋}. The corona of G and H is the graph G⊙H obtained by joining each vertex of G to all the vertices of a copy of H (Frucht and Harary, 1970). In this paper, we show that I(G⊙H;x) is palindromic for every graph G if and only if H=Kr-e,r≥2. In addition, we connect realrootness of I(G⊙H;x) with the same property of both I(G;x) and I(H;x).

Original languageEnglish
Pages (from-to)85-93
Number of pages9
JournalDiscrete Applied Mathematics
Volume203
DOIs
StatePublished - 20 Apr 2016

Keywords

  • Corona
  • Independence polynomial
  • Independent set
  • Palindromic polynomial
  • Perfect graph
  • Real root
  • Self-reciprocal sequence

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