G-2018-66
Maximum eccentric connectivity index for graphs with given diameter
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The eccentricity of a vertex \(v\)
in a graph \(G\)
is the maximum distance
between \(v\)
and any other vertex of \(G\)
. The diameter of a graph \(G\)
is
the maximum eccentricity of a vertex in \(G\)
. The eccentric connectivity
index of a connected graph is the sum over all vertices of the product
between eccentricity and degree. Given two integers \(n\)
and \(D\)
with \(D\leq n-1\)
, we characterize those graphs which have the largest
eccentric connectivity index among all connected graphs of order \(n\)
and
diameter \(D\)
. As a corollary, we also characterize those graphs which
have the largest eccentric connectivity index among all connected graphs
of a given order \(n\)
.
Paru en août 2018 , 14 pages