The minimum spectral radius of graphs with a given domination number

Abstract

Let Gn,γ be the set of simple and connected graphs on n vertices and with domination number γ. The graph with minimum spectral radius among Gn,γ is called the minimizer graph. In this paper, we first prove that the minimizer graph of Gn,γ must be a tree. Moreover, for γ∈{1,2,3,⌈n3⌉,⌊n2⌋}, we characterize all minimizer graphs in Gn,γ.