Bounds on hyper-status connectivity index of graphs

In this paper, we obtain the bounds for the hyper-status connectivity indices of a connected graph and its complement in terms of other graph invariants. In addition, the hyper-status connectivity indices of some composite graphs such as Cartesian product, join and composition of two connected graphs are obtained. We apply some of our results to compute the hyper-status connectivity indices of some important classes of graphs.Publisher's Versio

ZAGREB INDICES OF A NEW SUM OF GRAPHS

The first and second Zagreb indices, since its inception have been subjected to an extensive research in the physio- chemical analysis of compounds. In [6] Hanyuan Deng et.al computed the first and second Zagreb indices of four new operations on a graph defined by M. Eliasi, B. Taeri in [4]. Motivated from this we define a new operation on graphs and compute the first and second Zagreb indices of the resultant graph. We illustrate the results with some examples

Topological indices and f-polynomials on some graph products

We Obtain Inequalities Involving Many Topological Indices In Classical Graph Products By Using The F-Polynomial. In Particular, We Work With Lexicographic Product, Cartesian Sum And Cartesian Product, And With First Zagreb, Forgotten, Inverse Degree And Sum Lordeg Indices.Gobierno de Españ

Expected value of first Zagreb connection index in random cyclooctatetraene chain, random polyphenyls chain, and random chain network

The Zagreb connection indices are the known topological descriptors of the graphs that are constructed from the connection cardinality (degree of given nodes lying at a distance 2) presented in 1972 to determine the total electron energy of the alternate hydrocarbons. For a long time, these connection indices did not receive much research attention. Ali and Trinajstić [Mol. Inform. 37, Art. No. 1800008, 2018] examined the Zagreb connection indices and found that they compared to basic Zagreb indices and that they provide a finer value for the correlation coefficient for the 13 physico-chemical characteristics of the octane isomers. This article acquires the formulae of expected values of the first Zagreb connection index of a random cyclooctatetraene chain, a random polyphenyls chain, and a random chain network with l number of octagons, hexagons, and pentagons, respectively. The article presents extreme and average values of all the above random chains concerning a set of special chains, including the meta-chain, the ortho-chain, and the para-chain

Exploring Statistical and Population Aspects of Network Complexity

The characterization and the definition of the complexity of objects is an important but very difficult problem that attracted much interest in many different fields. In this paper we introduce a new measure, called network diversity score (NDS), which allows us to quantify structural properties of networks. We demonstrate numerically that our diversity score is capable of distinguishing ordered, random and complex networks from each other and, hence, allowing us to categorize networks with respect to their structural complexity. We study 16 additional network complexity measures and find that none of these measures has similar good categorization capabilities. In contrast to many other measures suggested so far aiming for a characterization of the structural complexity of networks, our score is different for a variety of reasons. First, our score is multiplicatively composed of four individual scores, each assessing different structural properties of a network. That means our composite score reflects the structural diversity of a network. Second, our score is defined for a population of networks instead of individual networks. We will show that this removes an unwanted ambiguity, inherently present in measures that are based on single networks. In order to apply our measure practically, we provide a statistical estimator for the diversity score, which is based on a finite number of samples