Connected graphs with a given dissociation number attaining the minimum spectral radius
Combinatorics
2023-09-28 v1
Abstract
A dissociation set of a graph is a set of vertices which induces a subgraph with maximum degree less than or equal to one. The dissociation number of a graph is the maximum cardinality of its dissociation sets. In this paper, we study the connected graphs of order with a given dissociation number that attains the minimum spectral radius. We characterize these graphs when the dissociation number is in . We also prove that these graphs are trees when the dissociation number is larger than .
Keywords
Cite
@article{arxiv.2309.15597,
title = {Connected graphs with a given dissociation number attaining the minimum spectral radius},
author = {Zejun Huang and Jiahui Liu and Xinwei Zhang},
journal= {arXiv preprint arXiv:2309.15597},
year = {2023}
}