Graphs of order n and diameter 2(n-1)/3 minimizing the spectral radius

2014/05/20 by Lan, Jingfen, Shi, Lingsheng
#Combinatorics (math.CO) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1405.5015

Abstract

The spectral radius of a graph is the largest eigenvalue of its adjacency matrix. A minimizer graph is such that minimizes the spectral radius among all connected graphs on n vertices with diameter d. The minimizer graphs are known for d∈\1,2\∪ [n/2,2n/3-1]∪\n-k| k=1,2,...,8\. In this paper, we determine all minimizer graphs for d=2(n-1)/3.

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