Year: 2026
Type: article
Abstract: For a graph G with any integer t ≥ 0, we denote by σt(G) the number of independent sets of size t in G. A Halin graph is a plane graph which consists of a plane embedding of a tree T of order at least 4 without a vertex of degree 2 and a cycle C connecting all leaves of T. In this paper we prove that the wheel uniquely maximizes the number of independent sets of given size at least 3 among all Halin graphs of fixed order. Moreover, two relevant problems are proposed to the number of independent sets of given size t.
Source: Ars Mathematica Contemporanea
Authors: Lihua Wei, Ximei Chen, Kexiang Xu
Institution: Nanjing University of Aeronautics and Astronautics
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7171540478
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