The Inverse Inertia Problem for Graphs

@inproceedings{Barrett2007TheII,
  title={The Inverse Inertia Problem for Graphs},
  author={Wayne Barrett and H. Tracy Hall and Raphael Loewy},
  year={2007}
}
Let G be an undirected graph on n vertices and let S(G) be the set of all real symmetric n × n matrices whose nonzero off-diagonal entries occur in exactly the positions corresponding to the edges of G. The inverse inertia problem for G asks which inertias can be attained by a matrix in S(G). We give a complete answer to this question for trees in terms of a new family of graph parameters, the maximal disconnection numbers of a graph. We also give a formula for the inertia set of a graph with a… CONTINUE READING

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