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Haemers, Willem H.
Discrete mathematics, October 2019, 2019-10-00, Letnik: 342, Številka: 10Journal Article
A mixed extension of a graph G is a graph H obtained from G by replacing each vertex of G by a clique or a coclique, where vertices of H coming from different vertices of G are adjacent if and only if the original vertices are adjacent in G. If G has no more than three vertices, H has all but at most three adjacency eigenvalues equal to 0 or −1. In this paper we consider the converse problem, and determine the class G of all graphs with at most three eigenvalues unequal to 0 and −1. Ignoring isolated vertices, we find that G consists of all mixed extensions of graphs on at most three vertices together with some particular mixed extensions of the paths P4 and P5.
