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

TL;DR

This paper characterizes the connected graphs with a fixed dissociation number that minimize spectral radius, using structural analysis and difference equations, specifically for dissociation number n-3.

Contribution

It provides a novel characterization of extremal graphs minimizing spectral radius for given dissociation number and connectivity.

Findings

Identifies extremal graphs with dissociation number n-3

Uses structure analysis and difference equations

Characterizes graphs minimizing spectral radius

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 $n-3$.