Abstract Analogues to multiplicative Zagreb indices in this paper two new type of eccentricity related topological index are introduced called the first and second multiplicative Zagreb eccentricity indices and is defined as product of squares of the eccentricities of the vertices and product of product of the eccentricities of the adjacent vertices. In this paper we give some upper and lower b...

In this paper, we defined a novel delta value di in molecular connectivity, and then obtained a novel kind of valence molecular connectivity index. The potential usefulness of the novel kind of valence molecular connectivity index in QSAR/QSPR is evaluated by its correlation with a number of molecules and by a favorable comparison with models based on molecular connectivity index. q 2003 Elsevi...

The mathematical properties of nano molecules are an interesting branch of nanoscience for researches nowadays. The periodic open single wall tubulene is one of the nano molecules which is built up from two caps and a distancing nanotube/neck. We discuss how to automatically construct the graph of this molecule and plot the graph by spring layout algorithm in graphviz and netwrokx packages. The...

The disk complex of a surface in a 3-manifold is used to define its topological index. Surfaces with well-defined topological index are shown to generalize well-known classes, such as incompressible, strongly irreducible, and critical surfaces. The main result is that one may always isotope a surface H with topological index n to meet an incompressible surface F so that the sum of the indices o...

The atom-bond connectivity (ABC) index is one of the most investigated degreebased molecular structure descriptors with a variety of chemical applications. It is known that among all connected graphs, the trees minimize the ABC index. However, a full characterization of trees with a minimal ABC index is still an open problem. By now, one of the proved properties is that a tree with a minimal AB...

Using the approach of mutual contribution of vertices to the value of topological indices derived from parts of a universal matrix gave the idea how to develop new topological indices. Some of the newly developed indices are useful indices of Octane Numbers and of Critical Pressure of alkanes of equal carbon number, giving rise to abs(Rfit) > 0.99. Using them we estimated the missing data of Oc...

The connectivity index wα(G) of a graph G is the sum of the weights (d(u)d(v)) of all edges uv of G, where α is a real number (α 6= 0), and d(u) denotes the degree of the vertex u. Let T be a tree with n vertices and k pendant vertices. In this paper, we give sharp lower and upper bounds for w1(T ). Also, for −1 ≤ α < 0, we give a sharp lower bound and a upper bound for wα(T ).

It is proved that any molecular graph invariant (that is any topological index) can be uniquely represented as (1) a linear combination of occurrence numbers of some substructures (fragments), both connected and disconnected, or (2) a polynomial on occurrence numbers of connected substructures of corresponding molecular graph. Besides, any (0,l)-valued molecular graph invariant can be uniquely ...

The topological index of a surface was previously introduced by the first author as the topological analogue of the index of an unstable minimal surface. Here we show that surfaces of arbitrarily high topological index exist. Consider a compact, connected, two sided surface S properly embedded in a compact, orientable 3-manifold M . The disk complex Γ(S) is the simplicial complex defined as fol...

Polynomial interpolation can be used to obtain closed formulas for topological indices of infinite series of molecular graphs. The method is discussed and its advantages and limitations are pointed out. This is illustrated on fullerenes C12k+4 and four topological indices: the Wiener index, the edge Wiener index, the eccentric connectivity index, and the reverse Wiener index. The results for th...