SFU Discrete Math Seminar: Kasra Masoudi

There is an interesting connection between chemistry and graph theory. This connection is highlighted by the relationship between a energy of a molecule and the eigenvalues of its graph. In the 1970s, a chemist named Ivan Gutman introduced a concept to define the energy of graphs, denoted as E(G). Simply put, Gutman’s definition involves adding up the absolute values of the eigenvalues of the graph’s adjacency matrix A. There exists a famous inequality on the energy of edge partitioning of Graphs, which states that energy of a graphs G is either less than or equal to the sum of the energies of its edge partitions. In this work, we show that in case of the connectivity of G the inequality is strict by using some features of positive semi-definite matrices and the relationship of the partitions with their adjacency matrices.