Algebraic Graph Theory Seminar - Soňa Pavlíková (20.4.2018)
Friday 20.4.2018 at 13:30, Lecture room M 213
By: Martin Mačaj
Soňa Pavlíková (Slovak University of Technology):
Construction of invertible graphs
The inverse of a graph with a non-singular adjacency matrix is another graph (uniquely determined by the original one up to isomorphism) whose spectrum consists precisely of the reciprocals of the eigenvalues of the original graph, including multiplicities. We will investigate the so-called positively and negatively invertible graphs. The class of negatively invertible graphs turns out to contain models of important organic molecules and invertibility allows to derive bounds on the binding energy of such molecules. We will present a fairly general construction of new invertible graphs based on `bridging' a pair of invertible graphs, which, informally, means `joining' the pair by a new bipartite graph attached to the two graphs at suitable subsets of vertices.