arXiv Analytics

Sign in

arXiv:1812.07199 [math.CO]AbstractReferencesReviewsResources

The Hessians of the complete and complete bipartite graphs and its application to the strong Lefschetz property

Akiko Yazawa

Published 2018-12-18Version 1

We consider the Hessian matrix of the weighted generating function for spanning trees. We call it the Hessian matrix of a graph. In this paper, we show that the Hessians of the complete and the complete bipartite graphs do not vanish by calculating the eigenvalues of the Hessian matrix of the graphs. As an application, we show the strong Lefschetz property for the Artinian Gorenstein algebra associated to the graphic matroids of the complete and complete bipartite graphs with at most five vertices.

Comments: 19 pages
Categories: math.CO, math.AC
Related articles: Most relevant | Search more
arXiv:1407.8537 [math.CO] (Published 2014-07-31)
A new application of the $\otimes_h$-product to $α$-labelings
arXiv:1210.6455 [math.CO] (Published 2012-10-24)
An application of a bijection of Mansour, Deng, and Du
arXiv:1509.04862 [math.CO] (Published 2015-09-16)
An application of the Local C(G,T) Theorem to a conjecture of Weiss

Links

Toolbox