Given a graph and set of Colors(0 to K-1). Now my task is to find the number of ways to color the graph nodes with maintaing the following conditions..

Let v be any vertex of the graph and u1, u2 ... um be the adjacent vertices of v, then

color(v) = color(u1) + color(u2) + ... + color(um) (modulo K)

Problem Link:source

How can i solve this problem using Gauss Elimination procedure. Thanks in advance.