MathDB

This problem is generalization of [url=http://www.mathlinks.ro/Forum/viewtopic.php?t=5918]this one. Suppose

G

is a graph and

S\subset 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\backslash S

that for each

v\in G\backslash S

number assigned to

v

is average of its neighbors.

Problem Statement