eccentric connectivity index: extremal graphs and values
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abstract
eccentric connectivity index has been found to have a low degeneracy and hence a significantpotential of predicting biological activity of certain classes of chemical compounds. wepresent here explicit formulas for eccentric connectivity index of various families of graphs.we also show that the eccentric connectivity index grows at most polynomially with thenumber of vertices and determine the leading coefficient in the asymptotic behavior.
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Eccentric Connectivity Index: Extremal Graphs and Values
Eccentric connectivity index has been found to have a low degeneracy and hence a significant potential of predicting biological activity of certain classes of chemical compounds. We present here explicit formulas for eccentric connectivity index of various families of graphs. We also show that the eccentric connectivity index grows at most polynomially with the number of vertices and determine ...
full textEccentric connectivity index: extremal graphs and values
Eccentric connectivity index has been found to have a low degeneracy and hence a significant potential of predicting biological activity of certain classes of chemical compounds. We present here explicit formulas for eccentric connectivity index of various families of graphs. We also show that the eccentric connectivity index grows at most polynomially with the number of vertices and determine ...
full textEccentric Connectivity Index of Some Dendrimer Graphs
The eccentricity connectivity index of a molecular graph G is defined as (G) = aV(G) deg(a)ε(a), where ε(a) is defined as the length of a maximal path connecting a to other vertices of G and deg(a) is degree of vertex a. Here, we compute this topological index for some infinite classes of dendrimer graphs.
full texteccentric connectivity index of some dendrimer graphs
the eccentricity connectivity index of a molecular graph g is defined as (g) = av(g)deg(a)ε(a), where ε(a) is defined as the length of a maximal path connecting a to othervertices of g and deg(a) is degree of vertex a. here, we compute this topological index forsome infinite classes of dendrimer graphs.
full textGraphs with Extremal Connectivity Index
Let G be a graph and δv the degree of its vertex v . The connectivity index of G is χ = ∑ (δu δv) −1/2 , with the summation ranging over all pairs of adjacent vertices of G . We offer a simple proof that (a) among n-vertex graphs without isolated vertices, the star has minimal χvalue, and (b) among n-vertex graphs, the graphs in which all components are regular of non–zero degree have maximal (...
full textOn the Eccentric Connectivity Index of Unicyclic Graphs
In this paper, we obtain the upper and lower bounds on the eccen- tricity connectivity index of unicyclic graphs with perfect matchings. Also we give some lower bounds on the eccentric connectivity index of unicyclic graphs with given matching numbers.
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Journal title:
iranian journal of mathematical chemistryPublisher: university of kashan
ISSN 2228-6489
volume 1
issue Issue 2 (Special Issue Dedicated to the Pioneering Role of Ivan Gutman In Mathematical Chemistry) 2010
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