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 language | English |
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Pages (from-to) | 108-116 |
Number of pages | 9 |
Journal | Carpathian Journal of Mathematics |
Volume | 23 |
Issue number | 1-2 |
State | Published - 2007 |
Keywords
- Clique-cover
- Independence polynomial
- Palindromic polynomial
- Real roots
- Stable set
- Uni-modality