%0 Journal Article
%T On Generalized Atom-bond Connectivity Index of Cacti
%J Iranian Journal of Mathematical Chemistry
%I University of Kashan
%Z 2228-6489
%A Hayat, Fazal
%D 2019
%\ 12/01/2019
%V 10
%N 4
%P 319-330
%! On Generalized Atom-bond Connectivity Index of Cacti
%K Atom-bond connectivity index
%K Cactus
%K Extremal graph
%K Pendant vertices
%R 10.22052/ijmc.2019.195759.1456
%X The generalized atom-bond connectivity index of a graph G is denoted by ABCa(G) and defined as the sum of weights ((d(u)+d(v)-2)/d(u)d(v))aa$ over all edges uv∊G. A cactus is a graph in which any two cycles have at most one common vertex. In this paper, we compute sharp bounds for ABCa index for cacti of order $n$ with fixed number of cycles and for cacti of order $n$ with given number of pendant vertices. Furthermore, we identify all the cacti that achieve the bounds.
%U https://ijmc.kashanu.ac.ir/article_102513_935bc1ec217d14c2928b98f54b69e2c5.pdf