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On the structure of graph edge designs that optimize the algebraic connectivity | IEEE Conference Publication | IEEE Xplore

On the structure of graph edge designs that optimize the algebraic connectivity


Abstract:

We take a structural approach to the problem of designing the edge weights in an undirected graph subject to an upper bound on their total, so as to maximize the algebrai...Show More

Abstract:

We take a structural approach to the problem of designing the edge weights in an undirected graph subject to an upper bound on their total, so as to maximize the algebraic connectivity. Specifically, we first characterize the eigenvector(s) associated with the algebraic connectivity at the optimum, using optimization machinery together with eigenvalue sensitivity notions. Using these characterizations, we fully address optimal design in tree graphs that is quadratic in the number of vertices, and also obtain a suite of results concerning the topological and eigen-structure of optimal designs for bipartite and general graphs.
Date of Conference: 09-11 December 2008
Date Added to IEEE Xplore: 06 January 2009
ISBN Information:
Print ISSN: 0191-2216
Conference Location: Cancun, Mexico

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