The Spectrum and Automorphism Group of the Set-Inclusion Graph

Abstract

Let [Formula: see text], [Formula: see text] and [Formula: see text] be integers with [Formula: see text]. The set-inclusion graph [Formula: see text] is the graph whose vertex set consists of all [Formula: see text]- and [Formula: see text]-subsets of [Formula: see text], where two distinct vertices are adjacent if one of them is contained in the other. In this paper, we determine the spectrum and automorphism group of [Formula: see text].