For a simple graph G

a graph G′is a spanning supergraph of G

if V(G′) = V(G)

E(G′) ? E(G).The degree d G(v) of a vertex v in G is the number of edges of G incident with v. In this paper

we study the problem that simple graphs have spanning supergraphs with the degree of each vertex divisible by 3. We completely characterize the spanning supergraphs of path graphs

star graphs and binary star graphs whose degree can be divided by 3. For general graph and tree graph

we give the sufficient conditions for the spanning supergraphs in which the degree of each vertex can be divided by 3.