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

Faculty of Mathematics and Informatics
Hanoi University of Science and Technology
Ariel University
Department of Computer Science
Holon Institute of Technology
Faculty of Education
An Giang University

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
Externally published	Yes

Bibliographical note

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

Keywords

Independence polynomial
clique corona graph
unimodality
well-covered graph

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10.26493/1855-3974.3383.3c7

Cite this

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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.

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KW - clique corona graph

KW - unimodality

KW - well-covered graph

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Unimodality of the independence polynomial of clique corona graphs

Abstract

Bibliographical note

Keywords

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