August 21, 2025Open Access

Signless Laplacian spectral radius for a k-extendable graph

Key Points

Lower bounds on the signless Laplacian spectral radius ensure k-extendability in certain graphs, indicating strong structural conditions.
Graphs must meet specific criteria related to perfect matching to validate the theoretical findings presented.
Analysis involves constructing extremal graphs to demonstrate the sharpness of the derived bounds on spectral radius.
Results contribute significant insights into graph theory, linking spectral properties to matching extensions in k-extendable graphs.

Abstract

Let k and n be two nonnegative integers with n ? 0 (mod 2), and let G be a graph of order n with a perfect matching. Then G is said to be k-extendable for 0 ? k ? n?2/2 if every matching in G of size k can be extended to a perfect matching. In this paper, we first establish a lower bound on the signless Laplacian spectral radius of G to ensure that G is k-extendable. Then we create some extremal graphs to claim that all the bounds derived in this article are sharp.

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Cite This Study

Zhou et al. (Wed,) studied this question.

synapsesocial.com/papers/68a6fb8c5502675167ba8b28 https://doi.org/https://doi.org/10.2298/fil2502649z

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