Nowadays, geospatial information systems (GIS) are widely used to solve different spatial problems based on various types of fundamental data: spatial, temporal, attribute and topological relations. Topological relations are the most important part of GIS which distinguish it from the other kinds of information technologies. One of the important mechanisms for representing topological relations...

The molecular topology of a graph is described by topological indices, which are numerical measures. In theoretical chemistry, indices quantities that used to represent the networks. These can be calculate several physical and chemical properties compounds, such as boiling point, entropy, heat generation, vaporization enthalpy. Graph theory comes in handy when looking at link between certain so...

the atom bond connectivity index of a graph is a new topological index was defined by e.estrada as abc(g)  uve (dg(u) dg(v) 2) / dg(u)dg(v) , where g d ( u ) denotes degreeof vertex u. in this paper we present some bounds of this new topological index.

The atom-bond connectivity (ABC) index is one of the recently most investigated degree-based molecular structure descriptors, that have applications in chemistry. For a graph G, the ABC index is defined as ∑ uv∈E(G) √ (d(u)+d(v)−2) d(u)d(v) , where d(u) is the degree of vertex u in G and E(G) is the set of edges of G. Despite many attempts in the last few years, it is still an open problem to c...

The degeneracy of topological distance sum (DS) and distance degree sequence (DDS) of small fullerenes is analyzed. The degeneracy of the two topological descriptors is determined by comparing the topological equivalence classes of the fullerene atoms with the DS and DDS classes, respectively. On the basis of DS and DDS degenerated fullerene graphs and by using two previously demonstrated theor...

the mathematical properties of nano molecules are an interesting branch of nanoscience forresearches nowadays. the periodic open single wall tubulene is one of the nano moleculeswhich is built up from two caps and a distancing nanotube/neck. we discuss how toautomatically construct the graph of this molecule and plot the graph by spring layoutalgorithm in graphviz and netwrokx packages. the sim...

In this paper, we present a new vision for studying ${F}$-open, ${F}$-continuous, and ${F}$-irresolute function in $(L,M)$-fuzzy topological spaces based on the implication operation and $(L,M)$-fuzzy ${F}$-open operator cite{2}. These kinds of functions are generalized with their elementary properties to $(L,M)$-fuzzy topological spaces setting based on graded concepts. Moreover, a systematic ...

Let G be a simple connected graph with n vertices and m edges and let d(e1) > d(e2) > · · · > d(em) be edge degree sequence of graph G. Denote by EF = ∑m i=1 d(ei) 3 reformulated forgotten index of G. Lower and upper bounds for the invariant EF are obtained.

We consider topological indices I that are sums of f(deg(u))f(deg(v)), where {u, v} are adjacent vertices and f is a function. The Randić connectivity index or the Zagreb group index are examples for indices of this kind. In earlier work on topological indices that are sums of independent random variables, we identified the correlation between I and the edge set of the molecular graph as the ma...