On the Difference Between the Eccentric Connectivity Index and Eccentric Distance Sum of Graphs

The eccentric connectivity index and second Zagreb eccentricity index are well-known graph invariants defined as the sums of contributions dependent on the eccentricities of adjacent vertices over all edges of a connected graph. The coindices of these invariants have recently been proposed by considering analogous contributions from the pairs of non-adjacent vertices. Here, we obtain several lower and upper bounds on the eccentric connectivity coindex and second Zagreb eccentricity coindex in terms of some graph parameters such as order, size, number of non-adjacent vertex pairs, radius, and diameter, and relate these invariants to some well-known graph invariants such as Zagreb indices and coindices, status connectivity indices and coindices, ordinary and multiplicative Zagreb eccentricity indices, Wiener index, degree distance, total eccentricity, eccentric connectivity index, second eccentric connectivity index, and eccentric-distance sum. Moreover, we compute the values of these coindices for two graph constructions, namely, double graphs and extended double graphs.

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On eccentricity-based topological descriptors of water-soluble dendrimers

Zeitschrift für Naturforschung C ◽

10.1515/znc-2018-0123 ◽

2018 ◽

Vol 74 (1-2) ◽

pp. 25-33 ◽

Cited By ~ 11

Author(s):

Zahid Iqbal ◽

Muhammad Ishaq ◽

Adnan Aslam ◽

Wei Gao

Keyword(s):

Molecular Structure ◽

Chemical Properties ◽

Topological Indices ◽

Water Soluble ◽

Connectivity Index ◽

Topological Descriptors ◽

Physical And Chemical Properties ◽

Eccentric Connectivity Index ◽

Physical And Chemical ◽

And Chemical Properties

AbstractPrevious studies show that certain physical and chemical properties of chemical compounds are closely related with their molecular structure. As a theoretical basis, it provides a new way of thinking by analyzing the molecular structure of the compounds to understand their physical and chemical properties. The molecular topological indices are numerical invariants of a molecular graph and are useful to predict their bioactivity. Among these topological indices, the eccentric-connectivity index has a prominent place, because of its high degree of predictability of pharmaceutical properties. In this article, we compute the closed formulae of eccentric-connectivity–based indices and its corresponding polynomial for water-soluble perylenediimides-cored polyglycerol dendrimers. Furthermore, the edge version of eccentric-connectivity index for a new class of dendrimers is determined. The conclusions we obtained in this article illustrate the promising application prospects in the field of bioinformatics and nanomaterial engineering.

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Ordering of alkane isomers by means of connectivity indices

Journal of the Serbian Chemical Society ◽

10.2298/jsc0202087g ◽

2002 ◽

Vol 67 (2) ◽

pp. 87-97 ◽

Cited By ~ 7

Author(s):

Ivan Gutman ◽

Dusica Vidovic ◽

Anka Nedic

Keyword(s):

Carbon Atom ◽

Organic Molecule ◽

Molecular Graph ◽

Connectivity Index ◽

Randić Index ◽

Randic Index ◽

Connectivity Indices ◽

The Difference

The connectivity index of an organic molecule whose molecular graph is Gis defined as C(?)=?(?u?v)??where ?u is the degree of the vertex u in G, where the summation goes over all pairs of adjacent vertices of G and where ? is a pertinently chosen exponent. The usual value of ? is ?1/2, in which case ?=C(?1/2) is referred to as the Randic index. The ordering of isomeric alkanes according to ??follows the extent of branching of the carbon-atom skeleton. We now study the ordering of the constitutional isomers of alkanes with 6 through 10 carbon atoms with respect to C(?) for various values of the parameter ?. This ordering significantly depends on ?. The difference between the orderings with respect to ??and with respect to C(?) is measured by a function ??and the ?-dependence of ??was established.

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