Abstract
The connective eccentricity index (CEI) of a connected graph
G
is defined as
ξ
ee
(
G
)
=
∑
u
∈
V
G
[
d
G
(
u
)
/
ε
G
(
u
)
]
, where
d
G
(
u
)
and
ε
G
(
u
)
are the degree and eccentricity, respectively, of the vertex
u
∈
V
G
of
G
. In this paper, graphs with the maximum CEI are characterized from the class of all connected graphs of a fixed order and size. Graphs having maximum CEI are also determined from some other well-known classes of connected graphs of a given order; namely, the Halin graphs, triangle-free graphs, planar graphs and outer-planar graphs.