This problem is generalization of [url=http://www.mathlinks.ro/Forum/viewtopic.php?t=5918]this one.
Suppose G is a graph and S⊂V(G). Suppose we have arbitrarily assign real numbers to each element of S. Prove that we can assign numbers to each vertex in G\S that for each v∈G\S number assigned to v is average of its neighbors. combinatorics proposedcombinatorics