Applications in chemistry motivated mathematicians to define different topological indices for types of graphs. The Hyper-Zagreb index (HM) is an important tool as it integrates the first and second Zagreb indices. In this paper, we characterize trees unicyclic graphs with four eight greatest HM-value, respectively.

In this note, we give expressions for the first(second) Zagreb coindex, second Zagreb index(coindex), third Zagreb index and first hyper-Zagreb index of the line graphs of subdivision graphs of 2D-lattice, nanotube and nanotorus of TUC4C8[p, q] and obtain upper bounds for Wiener index and degree-distance index of these graphs. This note continue the program of computing certain topological indi...

a topological index of a molecular graph g is a numeric quantity related to g which isinvariant under symmetry properties of g. in this paper we obtain the randić, geometricarithmetic,first and second zagreb indices , first and second zagreb coindices of tensorproduct of two graphs and then the harary, schultz and modified schultz indices of tensorproduct of a graph g with complete graph of ord...

let g be a simple connected graph. the first and second zagreb indices have been introducedas  vv(g)(v)2 m1(g) degg and m2(g)  uve(g)degg(u)degg(v) , respectively,where degg v(degg u) is the degree of vertex v (u) . in this paper, we define a newdistance-based named hyperzagreb as e uv e(g) .(v))2 hm(g)     (degg(u)  degg inthis paper, the hyperzagreb index of the cartesian product...

The area of graph theory (GT) is rapidly expanding and playing a significant role in cheminformatics, mostly mathematics chemistry to develop different physicochemical, chemical structure, their properties. manipulation study graphical details are made feasible by using numerical structure invariant. Investigating these characteristics topological indices (TIs) possible the discipline mathemati...

In this article, we calculate various topological invariants such as symmetric division degree index, redefined Zagreb VL first and second exponential multiplicative indices, entropy, entropies, entropy. We take the chemical compound named Proanthocyanidins, which is a very useful polyphenol in human’s diet. They are beneficial for one’s health. These compounds extracted from grape seeds. treme...

In this paper we study lower bounds in a unified way for large family of topological indices, including the first variable Zagreb index M 1 ? . Our aim is to obtain sharp inequalities and characterize corresponding extremal graphs. The main results provide several vertex-degree-based indices. These are new even Zagreb, inverse forgotten