G-2018-69
Minimum eccentric connectivity index for graphs with fixed order and fixed number of pending vertices
, , et référence BibTeX
The eccentric connectivity
index of a connected graph \(G\)
is the sum over all vertices \(v\)
of the product \(d_G(v)e_G(v)\)
, where \(d_G(v)\)
is the degree of \(v\)
in \(G\)
and \(e_G(v)\)
is the maximum distance
between \(v\)
and any other vertex of \(G\)
. This index is helpful for the prediction of biological activities
of diverse nature, a molecule being modeled as a graph where
atoms are represented by vertices and
chemical bonds by edges.
We characterize those graphs which
have the smallest eccentric connectivity index among all connected graphs of a given order \(n\)
. Also, given two integers \(n\)
and \(p\)
with \(p\leq n-1\)
, we characterize those graphs which have the smallest
eccentric connectivity index among all connected graphs of order \(n\)
with \(p\)
pending vertices.
Paru en septembre 2018 , 11 pages