Let Gbe a simple connected graph. A vertex vof Gis said to be a boundary vertex of another vertex uof Gif  for each neighbor wof v. If a vertex vis a boundary vertex of any vertex uof G, then it is said to be a boundary vertex of the graph G. In this paper, we define a vertex vof Gto be a strict boundary vertex of another vertex uof Gif  for each neighbor wof v. If a vertex vis a strict boundary vertex of any vertex uof G, then it is said to be a strict boundary vertex of the graph G. In this paper, we study the properties of strict boundary vertices of a graph.

distance, boundary, boundary vertex.