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In this paper we study the structure of some special bases for the null space of the incidence matrix of a graph. Recently it was shown that if G is a graph with no cut vertex, then G has a {−1,0,1}-basis. We generalize this result showing that the statement remains valid for every graph with no cut edge. For the null space of any bipartite graph, we construct a {−1,0,1}-basis. For any bipartite graph...
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