Constructing NSSD Molecular Graphs
İvan Gutman, Boris Furtula, Alexander Farrugia, Irene Sciriha · Croatica Chemica Acta · 2016
A graph is said to be non-singular if it has no eigenvalue equal to zero; otherwise it is singular.Molecular graphs that are non-singular and also have the property that all subgraphs of them obtained by deleting a single vertex are themselves singular, known as NSSD graphs, are of importance in the theory of molecular π-electron conductors; NSSD = non-singular graph with a singular deck.Whereas all non-singular bipartite graphs (therefore, the molecular graphs of all closed-shell alternant conjugated hydrocarbons) are NSSD, the non-bipartite case is much more complicated.Only a limited number of non-bipartite molecular graphs have the NSSD property.Several methods for constructing such molecular graphs are presented.