The signless Laplacian spectral radius of graphs with no intersecting triangles

2020/09/10 by Yanhua Zhao, Zhao, Yanhua, Xueyi Huang +3 · 1 citation
Mathematics · #05C50 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2009.04738

openalex publication_date 2020/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let F_k denote the k-fan consisting of k triangles which intersect in exactly one common vertex, and S_n,k the complete split graph of order n consisting of a clique on k vertices and an independent set on the remaining vertices in which each vertex of the clique is adjacent to each vertex of the independent set. In this paper, it is shown that S_n,k is the unique graph attaining the maximum signless Laplacian spectral radius among all graphs of order n containing no F_k, provided that k≥ 2 and n≥ 3k²-k-2.

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