Graphs for cone preserving maps

Abstract

Let K be a closed, pointed, full cone in a finite dimensional real vector space. We associate with a linear map A for which AK⊆ K four directed graphs. For two of the graphs the vertex set is the collection of all faces of K, and for two the vertices are all the extreme rays of K. We relate the irreducibility and primitivity of A to the strong connectedness of some of these graphs.