Maxima of the $Q$-index: Graphs with no $K_{1,t}$-minor

TL;DR

This paper characterizes the unique extremal graph with the highest $Q$-index among all $n$-vertex graphs that do not contain a $K_{1,t}$ minor, for $t \u2265 3$, advancing understanding of spectral extremal graph theory.

Contribution

It identifies the unique extremal graph maximizing the $Q$-index in the class of $K_{1,t}$-minor free graphs, a novel spectral extremal result.

Findings

Identifies the extremal graph with maximum $Q$-index among $K_{1,t}$-minor free graphs.

Provides a characterization of the extremal graph's structure.

Advances spectral extremal graph theory for minor-closed classes.

Abstract

A graph is said to be \textit{$H$-minor free} if it does not contain $H$ as a minor. In this paper, we characteristic the unique extremal graph with maximal $Q$-index among all $n$-vertex $K_{1,t}$-minor free graphs ($t\ge3$).