Maximum algebraic connectivity augmentation is NP-hard

Authors:
Damon Mosk-Aoyama
Affiliations:
Department of Computer Science, Stanford University, Gates Building, Room 460, 353 Serra Mall, Stanford, CA 94305, USA
Venue:
Operations Research Letters
Year:
2008

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Abstract

The algebraic connectivity of a graph, which is the second-smallest eigenvalue of the Laplacian of the graph, is a measure of connectivity. We show that the problem of adding a specified number of edges to an input graph to maximize the algebraic connectivity of the augmented graph is NP-hard.