Connected graphs minimizing the spectral radius for given order and dissociation number

Abstract

A dissociation set in a graph is a subset of vertices which induces a subgraph with maximum degree at most one. The dissociation number of a graph is the maximum cardinality of its dissociation sets. In this paper, we consider the $n$-vertex connected graphs with a given dissociation number that attain the minimum spectral radius. By using structure analysis and constructing difference equations, we characterize the extremal graphs with dissociation number $n-3$.

Added a missing co-author Jiahui Liu, who was unintentionally omitted from the author list in the previous version. Jiahui Liu has been included as an author in both the new and previous TeX source files