Spectral condition for spanning $k$-ended trees in $t$-connected graphs

TL;DR

This paper establishes a precise spectral radius condition that guarantees the existence of spanning trees with at most k leaves in t-connected graphs, extending previous results in spectral graph theory.

Contribution

It provides a tight spectral condition for spanning k-ended trees in t-connected graphs, generalizing earlier work by Ao, Liu, and Yuan (2023).

Findings

Spectral radius condition guarantees spanning k-ended trees.

The condition is tight and generalizes previous results.

Applicable to t-connected graphs with specified properties.

Abstract

For any integer $k\geq 2$, a spanning $k$-ended tree is a spanning tree with at most $k$ leaves. In this paper, we provide a tight spectral radius condition for the existence of a spanning $k$-ended tree in $t$-connected graphs, which generalizes a result of Ao, Liu and Yuan (2023).