The maximum number of maximum dissociation sets in potted graphs

Zejun Huang and Xinwei Zhang

Applied Mathematics and Computation, 2026, vol. 508, issue C

Abstract: A potted graph is a unicyclic graph such that its cycle contains a unique vertex with degree larger than 2. Given a graph G, a subset of V(G) is a dissociation set of G if it induces a subgraph with maximum degree at most one. A maximum dissociation set is a dissociation set with maximum cardinality. In this paper, we determine the maximum number of maximum dissociation sets in a potted graph of order n which contains a fixed cycle. The corresponding extremal graphs are also characterized.

Keywords: Dissociation number; Maximum dissociation set; Potted graph; Unicyclic graph (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:508:y:2026:i:c:s0096300325003443

DOI: 10.1016/j.amc.2025.129618

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