Constructions of graphs and trees with partially prescribed spectrum

2016/11/07 by Li, Xueliang, So, Wasin, Gutman, Ivan
#05C31 #05C50 #11C08 #15A18 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1611.01938

Abstract

It is shown how a connected graph and a tree with partially prescribed spectrum can be constructed. These constructions are based on a recent result of Salez that every totally real algebraic integer is an eigenvalue of a tree. Our result implies that for any (not necessarily connected) graph G, there is a tree T such that the characteristic polynomial P(G,x) of G can divide the characteristic polynomial P(T,x) of T, i.e., P(G,x) is a divisor of P(T,x).

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