Topological indices are quantitative measurements that describe a molecule’s topology and are quantified from the molecule’s graphical representation. The significance of topological indices is linked to their use in QSPR/QSAR modelling as descriptors. Mathematical associations between a particular molecular or biological activity and one or several biochemical and/or molecular structural features are QSPRs and QSARs. In this paper, we give explicit expressions of two recently defined novel ev-degree- and ve-degree-based topological indices of two classes of benzenoid, namely, linear hexagonal chain (...) and hammer-like benzenoid. (shrink)

For a graph G, its variable sum exdeg index is defined as SEI a G = ∑ x y ∈ E G a d x + a d y, where a is a real number other than 1 and d x is the degree of a vertex x. In this paper, we characterize all trees on n vertices with first three maximum and first three minimum values of the SEI a index. Also, we determine all the trees of order n (...) with given diameter d and having first three largest values of the SEI a index. (shrink)

A topological index is a numeric quantity related with the chemical composition claiming to correlate the chemical structure with different chemical properties. Topological indices serve to predict physicochemical properties of chemical substance. Among different topological indices, degree-based topological indices would be helpful in investigating the anti-inflammatory activities of certain chemical networks. In the current study, we determine the neighborhood second Zagreb index and the first extended first-order connectivity index for oxide network O X n, silicate network S L n, chain (...) silicate network C S n, and hexagonal network H X n. Also, we determine the neighborhood second Zagreb index and the first extended first-order connectivity index for honeycomb network H C n. (shrink)

A complete classification of simple function germs with respect to Lipschitz equivalence over the field of complex numbers ℂ was given by Nguyen et al. The aim of this article is to implement a classifier in terms of easy computable invariants to compute the type of the Lipschitz simple function germs without computing the normal form in the computer algebra system Singular.

In computer networks, vertices represent hosts or servers, and edges represent as the connecting medium between them. In localization, some special vertices are selected to locate the position of all vertices in a computer network. If an arbitrary vertex stopped working and selected vertices still remain the resolving set, then the chosen set is called as the fault-tolerant resolving set. The least number of vertices in such resolving sets is called the fault-tolerant metric dimension of the network. Because of the (...) variety of applications of the metric dimension in different areas of sciences, many generalizations were proposed, and fault tolerant is one of them. In this paper, we computed the fault-tolerant metric dimension of triangular snake, ladder, Mobius ladder, and hexagonal ladder networks. It is important to observe that, in all these classes of networks, the fault-tolerant metric dimension and metric dimension differ by 1. (shrink)