The maximum number of maximum dissociation sets in potted graphs
Combinatorics
2024-02-06 v1
Abstract
A potted graph is a unicyclic graph such that its cycle contains a unique vertex with degree larger than 2. Given a graph , a subset of is a dissociation set of 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 which contains a fixed cycle. Extremal potted graphs attaining this maximum number are also characterized.
Keywords
Cite
@article{arxiv.2402.02458,
title = {The maximum number of maximum dissociation sets in potted graphs},
author = {Zejun Huang and Xinwei Zhang},
journal= {arXiv preprint arXiv:2402.02458},
year = {2024}
}