The spectral radius of graphs without trees of diameter at most four

2016/10/04 by Hou, Xinmin, Liu, Boyuan, Wang, Shicheng +2 · 1 citation
#05C35 #05C50 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1610.00833

Abstract

Nikiforov (LAA, 2010) conjectured that for given integer k, any graph G of sufficiently large order n with spectral radius μ(G)≥ μ(S_n,k) contains all trees of order 2k+2, unless G=S_n,k, where S_n,k=K_k\vee K_n-k, the join of a complete graph of order k and an empty graph of order n-k. In this paper, we show that the conjecture is true for trees of diameter at most four.

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