the padmakar-ivan (pi) index is a wiener-szeged-like topological index which reflectscertain structural features of organic molecules. the pi index of a graph g is the sum of alledges uv of g of the number of edges which are not equidistant from the vertices u and v. inthis paper we obtain the second and third extremals of catacondensed hexagonal systems withrespect to the pi index.

Structural codes vis-a-vis structural counts, like polynomials of a molecular graph, are important in computing graph-theoretical descriptors which are commonly known as topological indices. These indices are most important for characterizing carbon nanotubes (CNTs). In this paper we have computed Sadhana index (Sd) for phenylenes and their hexagonal squeezes using structural codes (counts). Sa...

The enumeration of Kekule structures has fasci­ nated several researchers since the first systematic studies of benzenoids in terms of graph theory [1-9] , Apart from the recognized importance of Kekule structures in organic and physical chemistry they also have purely mathematical interest. Refer­ ence is made to a recent article in the present jo u r ­ nal [10] along with the bibliography the...

It is proved that a bipartite 2-connected plane graph in which the common boundary of adjacent faces is a simple curve is 1-cycle resonant if and only if the outer face of G is alternating and each inner vertex has degree two. This extends a result from [X. Guo, F. Zhang, k-cycle resonant graphs, Discrete Math. 135 (1994) 113-120] that a hexagonal system is 1-cycle resonant if and only if it is...

The Padmakar-Ivan (PI) index is a Wiener-Szeged-like topological index which reflects certain structural features of organic molecules. The PI index of a graph G is the sum of all edges uv of G of the number of edges which are not equidistant from the vertices u and v. In this paper we obtain the second and third extremals of catacondensed hexagonal systems with respect to the PI index.

We show that the molecular graph G of a benzenoid hydrocarbon admits an isometric embedding into the Cartesian product of three trees T1, T2, and T3 defined by three directions of the host hexagonal grid. Namely, to every vertex V of G one can associate an ordered triplet (V1, V2, V3) with Vi being a vertex of Ti (i ) 1, 2, 3), such that the graph-theoretic distance between two vertices u, V of...

Application of topological properties and graph theory to benzenoid hydrocarbons allowed us to construct an effective approach interpreting ring current formation in molecules when exposed to an external magnetic field. Transformation of unexcited canonical structures for molecules of 34 benzenoid hydrocarbons into circuit structures and then to directed circuit structures allowed us to define ...

Lei, Yeh and Zhang put forward the anti-forcing number af(G,M) for a perfect matching M in graph G, which is minimum of edges G not whose deletion results subgraph with unique M. The numbers all matchings form spectrum G. polynomial Af(G,x) counting classifying possessing same In this paper, we deduce recurrence formula continuity catacondensed hexagonal systems.

The importance of caterpillar trees in the topological theory of benzenoid systems lies in the following. Let B be a non-branched cata-condensed benzenoid hydrocarbon (that is a hydrocarbon containing linearly and angularly condensed rings). If we associate a symbol L to each linearly condensed ring (and also to the two terminal ones) and a symbol A to each angularly condensed ring, then the so...

Tessellations of kekulenes and cycloarenes have a lot potential as nanomolecular belts for trapping transporting heavy metal ions chloride because they the best electronic properties pore sizes. The aromaticity, superaromaticity, chirality, novel electrical magnetic class known been subject several experimental theoretical studies. Through topological computations superaromatic structures with ...