# Maximum Vertex Cover

Given a graph G=(V,E) and a positive weight function w on all the vertices, find a subset C from V such that all the edges (u,v) in E, at least one , u or v is contained in C and sum of all the weights of vertices in the set C is maximized.

For the Minimum Vertex Cover Problem, I used grMinVerCover (by calling grMinVerCover (E,w) ) function in Matlab. But I could not find a Maximum Vertex Cover function.

So, I calculated the reciprocal of the weights (w') of vertices in w, and then applied the vertex cover to E and w' by calling grMinVerCover(E,w'). The answers I am getting are correct but I want to know if this is logically correct?

Basically i need to find a Cover such that the number of vertices is minimized and the total weight is maximised.

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There needs to be more conditions on it than you've given - otherwise, doesn't choosing $C=V$ give you the best possible weight every time? –  Nicholas R. Peterson Jul 4 at 13:51
The problem requires that we create a set C which contains the minimum number of vertexes such that : 1)each edge (u,v) in E has at least one vertex u or v belonging to C. 2)And that the total weight of that set of vertices be maximum. These are the two conditions that define the problem. –  user2549925 Jul 4 at 14:33
Also posted at stackoverflow.com/users/2549925/user2549925 –  Falk Hüffner Jul 4 at 15:34