In this paper, we present some inequalities for the Co-PI index involving the some topological indices, the number of vertices and edges, and the maximum degree. After that, we give a result for trees. In addition, we give some inequalities for the largest eigenvalue of the Co-PI matrix of G.

In this paper, at first we mention to some results related to PI and vertex Co-PI indices and then we introduce the edge versions of Co-PI indices. Then, we obtain some properties about these new indices.

let g and h be two graphs. the corona product g o h is obtained by taking one copy of gand |v(g)| copies of h; and by joining each vertex of the i-th copy of h to the i-th vertex of g,i = 1, 2, …, |v(g)|. in this paper, we compute pi and hyper–wiener indices of the coronaproduct of graphs.

The performance of D-STATCOM depends on capacitor voltage regulation. In D-STATCOM, the nonlinear controller is preferred to linear controller. Regulating and fixing the capacitor DC voltage in DSTATCOM can improve the system dynamic such as capacitor voltage response, current response and modulation index. The regulation of DC capacitor voltage based on optimal PI co-efficient. In conventional...

the padmakar-ivan (pi) index is a first-generation topological index (ti) based on sums overall edges between numbers of edges closer to one endpoint and numbers of edges closer to theother endpoint. edges at equal distances from the two endpoints are ignored. an analogousdefinition is valid for the wiener index w, with the difference that sums are replaced byproducts. a few other tis are discu...

a lot of research and various techniques have been devoted for finding the topologicaldescriptor wiener index, but most of them deal with only particular cases. there exist threeregular plane tessellations, composed of the same kind of regular polygons namely triangular,square, and hexagonal. using edge congestion-sum problem, we devise a method to computethe wiener index and demonstrate this m...

General formulas are obtained for the vertex Padmakar-Ivan index (PIv) of tetrathiafulvalene (TTF) dendrimer, whereby TTF units we are employed as branching centers. The PIv index is a Wiener-Szeged-like index developed very recently. This topological index is defined as the summation of all sums of nu(e) and nv(e), over all edges of connected graph G.

in this paper, a new molecular-structure descriptor, the general sum–connectivity co–index  is considered, which generalizes the first zagreb co–index and the general sum–connectivity index of graph theory. we mainly explore the lower and upper bounds in termsof the order and size for this new invariant. additionally, the nordhaus–gaddum–type resultis also represented.