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

Vadim E. Levit; Eugen Mandrescu

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

Vadim E. Levit
, Eugen Mandrescu

Holon Institute of Technology
Ariel University

Research output: Contribution to journal › Article › peer-review

19 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 _αx^α, α = α(G), where s_k 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
Pages (from-to)	108-116
Number of pages	9
Journal	Carpathian Journal of Mathematics
Volume	23
Issue number	1-2
State	Published - 2007
Externally published	Yes

Keywords

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

Cite this

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title = "A family of graphs whose independence polynomials are both palindromic and unimodal",

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.",

keywords = "Clique-cover, Independence polynomial, Palindromic polynomial, Real roots, Stable set, Uni-modality",

author = "Levit, \{Vadim E.\} and Eugen Mandrescu",

year = "2007",

language = "אנגלית",

volume = "23",

pages = "108--116",

journal = "Carpathian Journal of Mathematics",

issn = "1584-2851",

publisher = "North University of Baia Mare",

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T1 - A family of graphs whose independence polynomials are both palindromic and unimodal

AU - Levit, Vadim E.

AU - Mandrescu, Eugen

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

KW - Clique-cover

KW - Independence polynomial

KW - Palindromic polynomial

KW - Real roots

KW - Stable set

KW - Uni-modality

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AN - SCOPUS:77953155894

SN - 1584-2851

VL - 23

SP - 108

EP - 116

JO - Carpathian Journal of Mathematics

JF - Carpathian Journal of Mathematics

IS - 1-2

ER -

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

Abstract

Keywords

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