Vertex-monochromatic connectivity of strong digraphs

Abstract A vertex coloring of a strong digraph D is a strong vertex-monochromatic connection coloring (SVMC-coloring) if for every pair u , v of vertices in D there exists an ( u , v ) -path having all its internal vertices of the same color. Let s m c v ( D ) denote the maximum number of colors used in an SVMC-coloring of a digraph D . In this paper we determine the value of s m c v ( D ) , whenever D is the line digraph of a digraph. Also, if T is a tournament, we give conditions to find the exact value of s m c v ( T ) .