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2017 On the maximal independence polynomial of certain graph configurations
Han Hu, Toufik Mansour, Chunwei Song
Rocky Mountain J. Math. 47(7): 2219-2253 (2017). DOI: 10.1216/RMJ-2017-47-7-2219

Abstract

In this paper, we investigate the maximal independence polynomials of some popular graph configurations. Through careful analysis, some of the polynomials under study are shown to be Chebyshev, which helps characterize polynomial properties such as unimodality, log-concavity and real-rootedness with ease and efficiency. We partially characterize the bridge path and bridge cycle graphs of wheels and fans according to their unimodality properties and propose relevant open problems. Also, to compare with the usual independence polynomials, we provide analogous results regarding the vertebrated graph, and the firecracker graph, as studied by Wang and Zhu~\cite {WZ11}.

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Han Hu. Toufik Mansour. Chunwei Song. "On the maximal independence polynomial of certain graph configurations." Rocky Mountain J. Math. 47 (7) 2219 - 2253, 2017. https://doi.org/10.1216/RMJ-2017-47-7-2219

Information

Published: 2017
First available in Project Euclid: 24 December 2017

zbMATH: 1378.05095
MathSciNet: MR3748229
Digital Object Identifier: 10.1216/RMJ-2017-47-7-2219

Subjects:
Primary: 05C31, 05C69, 42A05

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.47 • No. 7 • 2017
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