Weighted Laplacians and the Sigma Function of a Graph
نویسندگان
چکیده
We consider a general notion of the Laplacian of a graph. The weight of an edge reflects both the width and the length of an edge. Further, we allow the edge weights to vary in order to minimize the maximum eigenvalue, and using this minimum we construct the so-called σ−function of a graph. We consider a geometric interpretation of the σ−function, in particular as it applies to the detection of certain extremal configurations. Of special interest are σ−critical subgraphs. We derive several results about σ−critical graphs as well as offering conjectures about their structure. These results are related to applications in graph drawing algorithms and clique detection problems.
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