Abstract
An arithmetical structure on a finite, connected graph G is a pair of vectors (d,r) with positive integer entries for which (diag(d)−A(G))rT=0, where diag(d)=diag(d1,d2,…,dn),A(G) is the adjacency matrix of G and the entries of r have no common factor. In this paper, we will study the spectral radii of arithmetical structures on the path Pn and determine the arithmetical structures with the minimal and maximal spectral radius on Pn.
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