K e y w o r d s P l a n e graph, Outerplane graph, Bipartite graph, Perfect matching, Z-transformation graph. 1. I N T R O D U C T I O N A graph G is a planar graph if it can be embedded in plane such that edges only intersect at their end vertices. A plane graph is such an embedding. A plane graph is called an outerplane graph if all vertices are lie on the boundary of the exterior face. A gra...

Applying the recently obtained distributive lattice structure on the set of 1-factors, we show that the resonance graphs of any benzenoid systems G, as well as of general plane (weakly) elementary bipartite graphs, are median graphs and thus extend greatly Klavžar et al.’s result. The n-dimensional vectors of nonnegative integers as a labelling for the 1-factors of G with n inner faces are desc...

Localized molecular orbitals for n-systems of conjugated polycyclic hydrocarbons have been calculated using both intrinsic and external localization criteria relying only on molecular topology. For benzenoid aromatic compounds the intrinsic localized molecular orbital arrangement can always be associated to the Kekule structure of maximal Kekule index value. However hydrocarbons containing four...

We outline the construction of an algebraic (numerical) representation for Clar's valence formulas which in their geometrical form are illustrated with π-aromatic sextets as inscribed circles in benzenoid rings.

Graphene has been found to be an attractive material since its discovery in 2004 and has drawn enormous interest among researchers owing to its intrinsic electronic and magnetic properties. An indefinitely large graphene sheet, if cut along the two edge directions, can generate two distinct, well-defined small graphene nanoribbons (GNRs), which may be classified into “zigzag” edge (1, transpoly...