No abstract

The eccentric connectivity index ECI is a chemical structure descriptor that is currently being used for modeling of biological activities of a chemical compound. This index has been proved to provide a high degree of predictability compared to some other well-known indices in case of anticonvulsant, anti-inflammatory, and diuretic activities. The ECI of an infinite class of 1-polyacenic (phenylenic) nanotubes has been recently studied. In this study, we computed Ediz eccentric index and augmented eccentric connectivity index of Titania nanotube TiO2[m;n].

Topological index is a type of molecular descriptor calculated based on the molecular graph of a chemical compound. Topological indices are used for developing the quantitative structure activity relationships (QSARs) in which the biological activity or other properties of the molecules are correlated with their chemical structure. Eccentric connectivity indices are the well-known topological indices in this regards. In this research study, we computed some eccentric connectivity indices of the V-Phenylenic nanotube VPHX[p;q], these are our results.

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Let us consider a mapping [Formula: see text] of a graph [Formula: see text], where [Formula: see text] is an integer, [Formula: see text]. The mapping [Formula: see text] induces for every vertex [Formula: see text] of [Formula: see text] the label [Formula: see text]. Let [Formula: see text] ([Formula: see text]) denote the number of edges (vertices) in [Formula: see text] that are labeled with the number [Formula: see text] under the labeling [Formula: see text], [Formula: see text]. The function [Formula: see text] is called a [Formula: see text]-total edge product cordial labeling of [Formula: see text] if [Formula: see text] for [Formula: see text]. A graph [Formula: see text] with a [Formula: see text]-total edge product cordial labeling is called a [Formula: see text]-total edge product cordial graph. In this paper, we prove that the grid graph [Formula: see text] for [Formula: see text] admits a 3-total edge product cordial labeling.