Two Degree Distance Based Topological Indices of Chemical Trees

Let G = (V
_G
, E
_G
) be a simple and connected graph. The eccentric connectivity index of G is represented as ξ
^c
(G) = Σ
_x∈VG
deg
_G
(x)ec
_G
(x), where deg
_G
(x) and ec
_G
(x) represent the degree and the eccentricity of x, respectively. The eccentric adjacency index of G is represented as ξ
^ad
(G) = Σ
_x∈VG
(S
_G
(x)/ec
_G
(x)), where SQ(x) is the sum of degrees of neighbors of x. In this paper, we determine the trees with the smallest eccentric connectivity index when bipartition size, independence number, and domination number are given. Furthermore, we discuss the trees with the largest eccentric adjacency index when bipartition size, matching number, and independence number are given.