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<p>A dissociation set of a graph is a vertex subset whose induced subgraph has maximum degree at most one. The dissociation number of a graph is the cardinality of its largest dissociation set. In this paper, we establish both lower and upper bounds on the dissociation number of unicyclic graphs, parameterized by invariants such as maximum degree and diameter. We also characterize the structures of the extremal graphs attaining the upper bounds and the lower bounds.</p>

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Bounds on the Dissociation Number of Unicyclic Graphs

  • 期刊论文

  • 发表日期：

    2026年5月27日

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  • Wanyi Lai,
  • Jiahui Liu,
  • Zhenhua Lyu

摘要

A dissociation set of a graph is a vertex subset whose induced subgraph has maximum degree at most one. The dissociation number of a graph is the cardinality of its largest dissociation set. In this paper, we establish both lower and upper bounds on the dissociation number of unicyclic graphs, parameterized by invariants such as maximum degree and diameter. We also characterize the structures of the extremal graphs attaining the upper bounds and the lower bounds.