Augmented Eccentric Connectivity Index of Molecular Graph. [39] (original) (raw)
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Connective Eccentric Index of Circumcoronene Homologous Series of Benzenoid Hk. [95]
International Letters of Chemistry, Physics and Astronomy
Let G be a molecular graph, a topological index is a numeric quantity related to G which is invariant under graph automorphisms. The eccentric connectivity index ξ(G) is defined as ξ(G)= where dv, ε(v) denote the degree of vertex v in G and the largest distance between v and any other vertex u of G. The connective eccentric index of graph G is defined as Cξ(G)= In the present paper we compute the connective eccentric index of Circumcoronene Homologous Series of Benzenoid Hk (k≥1). Keywords: Molecular graphs, Benzenoid, Connective eccentric index, Eccentric connectivity index.
Modified Eccentric Connectivity polynomial of Circumcoronene Series of Benzenoid Hk. [74]
Journal of Advances in Physics
Let G=(V,E) be a molecular graph, where V(G) is a non-empty set of vertices/atoms and E(G) is a set of edges/bonds. For v V(G), defined dv be degree of vertex/atom v and S(v) is the sum of the degrees of its neighborhoods. The modified eccentricity connectivity polynomial of a molecular graph G is defined as where ε(v) is defined as the length of a maximal path connecting v to another vertex of molecular graph G. In this paper we compute this polynomial for a famous molecular graph of Benzenoid family. Indexing terms/Keywords Molecular graph; Circumcoronene Series of benzenoid; Modified Eccentricity Connectivity polynomial.
Annals of West University of Timisoara-Mathematics and Computer Science, 2013
Let G = (V, E) be a simple connected molecular graph. In such a simple molecular graph, vertices represent atoms and edges represent chemical bonds, we denoted the sets of vertices and edges by V = V (G) and E = E(G), respectively. If d(u, v) be the notation of distance between vertices u, v ∈ V and is defined as the length of a shortest path connecting them. Then, Eccentricity connectivity polynomial of a molecular graph G is defined
Eccentricity Version of Atom-Bond Connectivity Index of Benzenoid Family ABC5(Hk). [30]
World Applied Sciences Journal, 2013
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 graph G, (G) and defined as where ecc(u) is the largest distance between u and any other vertex v of G. And if then the distance d(x,y) between x and y is defined as the length of any shortest path in G connecting x and y. Now, by combine these above topological indexes, we now define a new version of ABC index as We denote this new index of a connected graph G (eccentric atom-bond connectivity index) by ABC (G). In this paper, we exhibit this new index and introduce 5 a closed formula of ABC for a famous family of Benzenoid. 5
International Journal of Chemical Modeling (Nova)
Let G=(V; E) be a simple connected graph. The sets of vertices and edges of G are denoted by V=V(G) and E=E (G), respectively. In such a simple molecular graph, vertices represent atoms and edges represent bonds. In graph theory, we have many invariant polynomials and topological indices for a graph. In this paper, we focus on the structure of molecular graph "Circumcoronene series of benzenoid H k (k≥1)" and counting Randic index Geometric-Arithmetic index and Atom-Bond Connectivity index
On the Eccentric Connectivity Index of Certain Molecular Graphs
2011
A simple graph ) , ( = E V G is a finite nonempty set ) (G V of objects called vertices together with a (possibly empty) set ) (G E of unordered pairs of distinct vertices of G called edges. In chemical graphs, the vertices of the graph correspond to the atoms of the molecule, and the edges represent the chemical bonds. If ) ( , G V y x ∈ then the distance ) , ( y x d between x and y is defined as the length of a minimum path connecting x and y . The eccentric connectivity index of the molecular graph G , ) (G c ξ , was proposed by Sharma, Goswami and Madan 8. It is defined as ) ( ) ( ) ( = ) ( u ecc u G deg G V u G c ∑ ∈ ξ , where ) (x G deg denotes the degree of the vertex x in G