Southeast Asian Bulletin of

Abstract. For each graph parameter f = f(G) of a graph G, it is said that f interpolates over the set of all graphs with a fixed degree sequence d, R(d) if the following statement holds: If m and M are the minimum and maximum values (respectively) of f(G) over all G ∈ R(d), then for any k, m ≤ k ≤ M, there is a graph G ∈ R(d) such that f(G) = k. In this paper, three graph parameters are shown to be interpolating, namely the vertex independence number, the edge independence number (or matching number) and the vertex domination number. Relevant graph parameters are also discussed, some of which are shown to be interpolating while some are not