Quadratic embedding constants of path graphs
Wojciech M{\l}otkowski
TL;DR
This paper characterizes positive definiteness of certain matrices and applies this to explicitly compute the quadratic embedding constants of path graphs.
Contribution
It provides a new characterization of positive definite matrices and derives explicit quadratic embedding constants for path graphs.
Findings
Explicit quadratic embedding constants for path graphs
New characterization of positive definite matrices
Application to graph embedding problems
Abstract
We characterize positive definiteness for some family of matrices. As an application we derive explicit value of the quadratic embedding constants of the path graphs.
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Taxonomy
TopicsGraph theory and applications · Matrix Theory and Algorithms · Advanced Topics in Algebra