Laplacian Eigenvalues of Threshold Graphs
Several problems in mathematics can be viewed as completion problems. Matrix theory is particularly rich in such problems. Such problems nicely blend graph theoretic notions with matrix theory. In this chapter we consider one particular completion problem, the positive definite completion problem, in detail. We first illustrate the concept of matrix completion by considering the nonsingular completion problem. We then introduce the preliminaries on chordal graphs. Then we prove the main result that a graph is positive definite completable if and only if it is chordal.
References and Further Reading
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