Abstract. A subgraph H of a graph G is gated if for every x ∈ V (G) there exists a vertex u in H such that dG(x, v) = dG(x, u) + dG(u, v) for any v ∈ V (H). The gated amalgam of graphs G1 and G2 is obtained from G1 and G2 by identifying their isomorphic gated subgraphs H1 and H2. Two theorems on the Wiener index of gated amalgams are proved. Several known results on the Wiener index of (chemica...

We report the syntheses and properties of thienopyrrole based unsymmetrical and extended heteroacenes, which are isoelectronic with heptacene (30π) and nonacene (38π), respectively. Optical and electrochemical properties of these seven and nine rings fused systems are studied. The optoelectronic properties of the syn and anti-isomers of the unsymmetrical heteroacenes are also compared. The infl...

Non-alternant non-benzenoid hydrocarbons exhibit very different optical and electronic properties than their well-studied benzenoid analogues. However, preparing such structures with extended conjugation length, remains challenging. Herein, we report the synthesis of azuleno[2,1,8-ija]azulene derivatives using a two-step sequence involving four-fold aldol condensation between aromatic dialdehyd...

the tutte polynomial of a graph g, t(g, x,y) is a polynomial in two variables defined for every undirected graph contains information about how the graph is connected. in this paper a simple formula for computing tutte polynomial of a benzenoid chain is presented.

Titrations of actinomycin D (AMD) with dG and with dG-dC were monitored by circular dichroism at 380 nm and 470 nm. These wavelengths are sensitive predominantly to nucleotide binding processes at the benzenoid and quinoid portions, respectively, of the phenoxazone ring of the drug chromophore [Auer, H.E., Pawlowski-Konopnicki, B.E., Chiao, Y.C.C. & Krugh, T.R. (1978), Biopolymers, 17, 1891-191...

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...

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.