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 sequence of all paths pi of lengths i = 1 to the maximum possible length in a hydrogen-depleted molecular graph (which sequence is also called the molecular path code) contains significant information on the molecular topology, and as such it is a reasonable choice to be selected as the basis of topological indices (TIs). Four new (or five partly new) TIs with progressively improved perform...

In this paper, we derive interrelations of graph distance measures by means of inequalities. For this investigation we are using graph distance measures based on topological indices that have not been studied in this context. Specifically, we are using the well-known Wiener index, Randić index, eigenvalue-based quantities and graph entropies. In addition to this analysis, we present results fro...

For a connected graph G, the eccentric connectivity index (ECI) and the first Zagreb eccentricity index of G are defined as ( ) ( ) deg ( ) ( ) i c G i G i v V G ξ G v ε v   and ( 2 1 ) ( ) ( ) i G i v G V E G ε v   , respectively, where deg ( ) G i v is the degree of i v in G and ( ) G i ε v denotes the eccentricity of vertex i v in G. In this paper we compare the eccentric connectivity ...

the time evaluation of quantum entropy in a four-level double- type atomic system is theoretically investigated. quantum entanglement of the atom and its spontaneous emission fields is then discussed via quantum entropy. it is found that the degree of entanglement can be increased by the quantum interference induced by spontaneous emission. the phase dependence of the atom-field entanglement is...

Among topological descriptors, connectivity indices are very important and they have a prominent role in chemistry. One of them is atom-bond connectivity (ABC) index of a connected graph G=(V,E) and defined as where d denotes the degree of vertex v of G, that introduced by Furtula v and et.al. Also, in 1997, Sharma, Goswami and Madan introduced the eccentric connectivity index of the molecular ...