Abstract: The extended profile problem is to find a proper interval supergraph with the smallest possible number of edges. The problem stems from the storage and elimination techniques of a sparse symmetric matrix A in 1950's. It has important applications in numerical algebra, VLSI designs and molecular biology. A tree T is a connected acyclic graph. The complement of a tree T is called a co-tree, denoted by Tˉ. In this paper the exact extended profile value of a cotree Tˉ is given.

Key words:  the proper interval graph, the extended profile, tree, co-tree