A New Class of Almost Controllable Graphs

Abstract

A graph G is called a chain graph if it contains none of the graphs {2K2,C3,C5} as induced subgraphs. It is said to be almost controllable if it has exactly one non-main eigenvalue, that is, precisely one eigenvalue whose corresponding eigenspace is orthogonal to the all-ones vector. Within the class of chain graphs, we identify new families of graphs exhibiting this almost controllable property.