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On the rank of weighted graphs. (English) Zbl 1356.05067
Summary: Let \(G_w\) be a weighted graph and \(A(G_w)\) be the adjacency matrix of \(G_w\). The rank of \(G_w\) is the rank of \(A(G_w)\). If the weight of each edge of \(G_w\) is 1 or \(-1\), \(G_w\) is also called a signed graph. In this paper, we characterize weighted graphs with rank 2, weighted \(K_4\)-free graphs with rank 3 and weighted graphs containing pendent vertices with rank 4. We also characterize signed graphs with rank 4.

MSC:
05C22 Signed and weighted graphs
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
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