Graphs and irreducible cone preserving maps

[[abstract]]Let K be a full, pointed closed cone in a finite dimensional real vector space. For any linear map A for which AK⊆K, denote by (E,P(A)[E,I (A))] the directed graph whose vertex set consists of all the extreme rays of K such that there is an edge from F to G iff . It is proved that K is a simplicial cone if for any linear map A with is strongly connected whenever A is irreducible [provided, in addition, that K is 2-neighborly].[[notice]]補正完畢[[journaltype]]國外[[incitationindex]]SC