Unimodality of the Independence Polynomial of G∘(Kp∪Kq)

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

doi:10.1007/s10013-024-00723-w

Unimodality of the Independence Polynomial of G∘(Kp∪Kq)

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

Department of Mathematics

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

Abstract

In this paper, our research primarily focuses on f-symmetric and unimodal properties of independence polynomials I(G∘(K_p∪K_q);x). More precisely, we prove that the independence polynomial I(G∘(K_p∪K_q);x) is unimodal for every graph G, whenever the positive integers p and q are large enough. In addition, we establish several inequalities involving the coefficients of I(G∘(K_p∪K_q);x) for arbitrary p and q.

Original language	English
Journal	Vietnam Journal of Mathematics
DOIs	https://doi.org/10.1007/s10013-024-00723-w
State	Accepted/In press - 2024

Keywords

05C31
13C14
Independence polynomial
Primary: 05C69
Secondary: 05C30
Unimodality
f-symmetric polynomial

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10.1007/s10013-024-00723-w

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title = "Unimodality of the Independence Polynomial of G∘(Kp∪Kq)",

abstract = "In this paper, our research primarily focuses on f-symmetric and unimodal properties of independence polynomials I(G∘(Kp∪Kq);x). More precisely, we prove that the independence polynomial I(G∘(Kp∪Kq);x) is unimodal for every graph G, whenever the positive integers p and q are large enough. In addition, we establish several inequalities involving the coefficients of I(G∘(Kp∪Kq);x) for arbitrary p and q.",

keywords = "05C31, 13C14, Independence polynomial, Primary: 05C69, Secondary: 05C30, Unimodality, f-symmetric polynomial",

author = "Hoang, {Do Trong} and Levit, {Vadim E.} and Eugen Mandrescu and Pham, {My Hanh}",

note = "Publisher Copyright: {\textcopyright} Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2024.",

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AU - Hoang, Do Trong

AU - Levit, Vadim E.

AU - Mandrescu, Eugen

AU - Pham, My Hanh

N1 - Publisher Copyright: © Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2024.

PY - 2024

Y1 - 2024

N2 - In this paper, our research primarily focuses on f-symmetric and unimodal properties of independence polynomials I(G∘(Kp∪Kq);x). More precisely, we prove that the independence polynomial I(G∘(Kp∪Kq);x) is unimodal for every graph G, whenever the positive integers p and q are large enough. In addition, we establish several inequalities involving the coefficients of I(G∘(Kp∪Kq);x) for arbitrary p and q.

AB - In this paper, our research primarily focuses on f-symmetric and unimodal properties of independence polynomials I(G∘(Kp∪Kq);x). More precisely, we prove that the independence polynomial I(G∘(Kp∪Kq);x) is unimodal for every graph G, whenever the positive integers p and q are large enough. In addition, we establish several inequalities involving the coefficients of I(G∘(Kp∪Kq);x) for arbitrary p and q.

KW - 05C31

KW - 13C14

KW - Independence polynomial

KW - Primary: 05C69

KW - Secondary: 05C30

KW - Unimodality

KW - f-symmetric polynomial

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DO - 10.1007/s10013-024-00723-w

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AN - SCOPUS:85209543130

SN - 2305-221X

JO - Vietnam Journal of Mathematics

JF - Vietnam Journal of Mathematics

ER -

Unimodality of the Independence Polynomial of G∘(Kp∪Kq)

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