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 dG(v)eG(v)
, where dG(v)
is the degree of v
in G
and eG(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≤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