What question did this study set out to answer?

The aim is to establish tight spectral radius conditions for the presence of spanning k-ended trees in t-connected graphs.

February 28, 2026

Spectral Condition for Spanning k-Ended Trees in t-Connected Graphs

Key Points

The aim is to establish tight spectral radius conditions for the presence of spanning k-ended trees in t-connected graphs.
Defined k-ended trees with specified leaf limits.
Analyzed spectral radius conditions relevant to graph connectivity.
Generalized prior results in graph theory regarding spanning trees.
Identified exact conditions under which spanning k-ended trees exist in t-connected graphs.
Showed how these conditions improve upon previous findings in the literature.

Abstract

For any integer Formula: see text, a spanning Formula: see text-ended tree is a spanning tree with at most Formula: see text leaves. In this paper, we provide tight spectral radius conditions for the existence of a spanning Formula: see text-ended tree in Formula: see text-connected graphs, which generalizes a result of Ao, Liu and Yuan (2023).

Spectral Condition for Spanning k-Ended Trees in t-Connected Graphs

Key Points

Abstract

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