[PDF] Top 20 Eccentric Connectivity Index: Extremal Graphs and Values

... Let G be a graph on n vertices. We denote the vertex and the edge set of G by V(G) and E(G), respectively. For two vertices u and v of V(G) we define their distance d(u,v) as the length of any shortest path connecting u ... See full document

... detour eccentric connectivity index and detour connective eccentric index of ...The values of these indices for some common graphs are ... See full document

... the extremal values of the invariant and the extremal graphs where those values are achieved, also in a number of explicit formulas for the eccentric connectivity ... See full document

... Gutman index of graphs, we proposed the degree-distance of a graph to a vertex and the vertex-Gutman ...the extremal values and rankings of the vertex-Gutman indices of the k-caterpillar, ... See full document

... the extremal values (vertex) and rankings of the vertex-degree-distance of the ...the extremal values (vertex) and extremal graphs of the vertex-degree-distance of other similar ... See full document

... (SDD) index was selected as a significant predictor of total surface area of polychlorobiphenyls ...its extremal graphs obtained with the help of MathChem [10] have particularly simple and elegant ... See full document

... analyze extremal values and extremal graphs for many topological indices on the spiro and polyphenyl hexagonal ...Simmons index, Hosoya index, Wiener index and Kirchhoff ... See full document

... this index first appeared in [4]. Zhong found the minimum and maximum values of the harmonic index for simple connected graphs, trees and unicyclic graphs and characterized the ... See full document

... of graphs with somewhat similar properties (planar graphs whose all bounded faces are cycles of length 6) known as benzenoid graphs, has been studied for a long time as the mathematical model of a ... See full document

... eccentricity connectivity index of unicyclic graphs with perfect ...the eccentric connectivity index of unicyclic graphs with given matching ... See full document

... A topological index is a numerical descriptor of the molecular structure derived from the corresponding (hydrogen-depleted) molecular graph. Various topological indices are widely used for quantitative ... See full document

... of graphs with very many interesting ...of graphs is the class of broom graphs (see for example [4, 6, 8, 9]) which are in fact one of the types of chemical trees ...an eccentric graph of a ... See full document

... some eccentric-based topological ...of eccentric-based indices of some ...augmented eccentric connectivity index of two classes of fullerene graphs C ... See full document

... Several extremal properties of the sum-connectivity index and general sum-connectivity index for trees, unicyclic graphs, -connected graphs and bicyclic graphs ... See full document

... fullerene graphs is for their applications in fullerene ...fullerene graphs are a new branch of nanoscience started by pioneering work of Fowler et ... See full document

... A topological index, known as eccentric connectivity index, studies the molecular structure of graphs [4]. For basic definitions and notations, refer to [1]. For any simple connected ... See full document

... molecular graphs have been studied in terms of topological indices that are numeric quantities developed as molecular ...The eccentric con- nectivity index is a parameter recently introduced [10] and ... See full document

... Trees are defined as connected graphs without cycles. Recursive trees are rooted labelled trees, where the root is labelled by 1 and the labels of all successors of any node v are larger than the label of v [10]. ... See full document

... By a graph means a set of vertices and edges which denotes by V(G) and E(G), respectively. If e is an edge of G, connecting the vertices u and v, then we write e = uv and say "u and v are adjacent". A connected ... See full document

... topological index. The Wiener index [1] is the first reported distance based topological index defined as half sum of the distances between all the pairs of vertices in a molecular graph ... See full document