Unimodality of the independence polynomial of clique corona graphs

Do Trong Hoang; Vadim E. Levit; Eugen Mandrescu; My Hanh Pham

doi:10.26493/1855-3974.3383.3c7

Unimodality of the independence polynomial of clique corona graphs

Do Trong Hoang
, Vadim E. Levit
, Eugen Mandrescu
, My Hanh Pham

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

Abstract

For a positive integer p, a graph G belongs to the class W_p if |V (G)| ≥ p and any p disjoint independent sets can be extended to p disjoint maximum independent sets. In this paper, we establish several inequalities for the coefficients of the independence polynomial of graphs in W_p. We then prove that the clique corona graph G ◦ K_p, formed from a graph G and a complete graph K_p, also belongs to W_p. As an application, we examine the unimodality problem for the independence polynomial of G ◦ K_p. In particular, we prove that the independence polynomial of S_n ◦ K_p, where S_n is a star graph, is unimodal.

Original language	English
Journal	Ars Mathematica Contemporanea
DOIs	https://doi.org/10.26493/1855-3974.3383.3c7
State	Published - 2026

Keywords

clique corona graph
Independence polynomial
unimodality
well-covered graph

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10.26493/1855-3974.3383.3c7

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abstract = "For a positive integer p, a graph G belongs to the class Wp if |V (G)| ≥ p and any p disjoint independent sets can be extended to p disjoint maximum independent sets. In this paper, we establish several inequalities for the coefficients of the independence polynomial of graphs in Wp. We then prove that the clique corona graph G ◦ Kp, formed from a graph G and a complete graph Kp, also belongs to Wp. As an application, we examine the unimodality problem for the independence polynomial of G ◦ Kp. In particular, we prove that the independence polynomial of Sn ◦ Kp, where Sn is a star graph, is unimodal.",

keywords = "clique corona graph, Independence polynomial, unimodality, well-covered graph",

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TY - JOUR

T1 - Unimodality of the independence polynomial of clique corona graphs

AU - Hoang, Do Trong

AU - Levit, Vadim E.

AU - Mandrescu, Eugen

AU - Pham, My Hanh

N1 - Publisher Copyright: This work is licensed under https://creativecommons.org/licenses/by/4.0/

PY - 2026

Y1 - 2026

N2 - For a positive integer p, a graph G belongs to the class Wp if |V (G)| ≥ p and any p disjoint independent sets can be extended to p disjoint maximum independent sets. In this paper, we establish several inequalities for the coefficients of the independence polynomial of graphs in Wp. We then prove that the clique corona graph G ◦ Kp, formed from a graph G and a complete graph Kp, also belongs to Wp. As an application, we examine the unimodality problem for the independence polynomial of G ◦ Kp. In particular, we prove that the independence polynomial of Sn ◦ Kp, where Sn is a star graph, is unimodal.

AB - For a positive integer p, a graph G belongs to the class Wp if |V (G)| ≥ p and any p disjoint independent sets can be extended to p disjoint maximum independent sets. In this paper, we establish several inequalities for the coefficients of the independence polynomial of graphs in Wp. We then prove that the clique corona graph G ◦ Kp, formed from a graph G and a complete graph Kp, also belongs to Wp. As an application, we examine the unimodality problem for the independence polynomial of G ◦ Kp. In particular, we prove that the independence polynomial of Sn ◦ Kp, where Sn is a star graph, is unimodal.

KW - clique corona graph

KW - Independence polynomial

KW - unimodality

KW - well-covered graph

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Unimodality of the independence polynomial of clique corona graphs

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