Spectral conditions for spanning $k$-trees or $k$-ended-trees of $t$-connected graphs

TL;DR

This paper provides spectral criteria for the existence of spanning $k$-trees and $k$-ended-trees in $t$-connected graphs, generalizing and improving previous results in graph theory.

Contribution

It introduces new spectral conditions that guarantee the presence of spanning $k$-trees or $k$-ended-trees in highly connected graphs, extending prior work.

Findings

Established spectral conditions for spanning $k$-trees.

Extended results to spanning $k$-ended-trees.

Improved upon previous theorems in spectral graph theory.

Abstract

Let $G$ be a connected graph of order $n$. A spanning $k$-tree of $G$ is a spanning tree with the maximum degree at most $k$, and a spanning $k$-ended-tree of $G$ is a spanning tree at most $k$ leaves, where $k\geq2$ is an integer. This paper establishes some spectral conditions for the existence of spanning $k$-trees or spanning $k$-ended-trees in $t$-connected graphs, which generalize the results of Fan et al. (2022) and Zhou (2010), and improve the results of Fiedler et al. (2010), Ao et al. (2023) and Ao et al. (2025).