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arXiv · 2108.03895

The signless Laplacian spectral radius of graphs without intersecting odd cycles

Ming-Zhu Chen·A-Ming Liu·Xiao-Dong Zhang
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Abstract

Let $F_{a_1,\dots,a_k}$ be a graph consisting of $k$ cycles of odd length $2a_1+1,\dots, 2a_k+1$, respectively which intersect in exactly a common vertex, where $k\geq1$ and $a_1\ge a_2\ge \cdots\ge a_k\ge 1$. In this paper, we present a sharp upper bound for the signless Laplacian spectral radius of all $F_{a_1,\dots,a_k}$-free graphs and characterize all extremal graphs which attain the bound. The stability methods and structure of graphs associated with the eigenvalue are adapted for the proof.

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Ming-Zhu Chen, A-Ming Liu, Xiao-Dong Zhang. 2021-08-09. The signless Laplacian spectral radius of graphs without intersecting odd cycles. https://arxiv.org/abs/2108.03895

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