On the minimum spectral radius of graphs with given order and dissociation number

Abstract

A dissociation set in a graph $G$ is a set of vertices that induces a subgraph of maximum degree at most 1. The cardinality of a maximum dissociation set in $G$ is called the dissociation number of $G$. Huang et al. determined the graphs with the minimum spectral radius among all connected graphs with given order $n$ and dissociation number $2,\lceil \frac{2n}{3}\rceil ,n-2,n-1$, respectively. In this paper, we characterize the graphs that attain the minimum spectral radius among all connected graphs with given order $n$ and dissociation number $\lceil \frac{2n}{3}\rceil -1$.