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arXiv · 2606.28121

The Signless Laplacian Spectral Radius of $tK_3$-Free Graphs

Jing Zeng
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Abstract

The signless Laplacian matrix of a graph $G$ is $Q(G)=D(G)+A(G)$, where $D(G)$ and $A(G)$ are the diagonal degree matrix and the adjacency matrix of $G$, respectively. The signless Laplacian spectral radius of $G$ is the largest eigenvalue of $Q(G)$. For a positive integer $t$, a graph is called $tK_3$-free if it contains no $t$ vertex-disjoint triangles. In this paper, for every fixed $t\geq 2$ and all $n\geq 28t-17$, we determine the unique graph achieving the maximum signless Laplacian spectral radius among all $tK_3$-free graphs of order $n$.

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Jing Zeng. 2026-06-26. The Signless Laplacian Spectral Radius of $tK_3$-Free Graphs. https://arxiv.org/abs/2606.28121

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