University of KashanIranian Journal of Mathematical Chemistry2228-648910420191201On Generalized Atom-bond Connectivity Index of Cacti31933010251310.22052/ijmc.2019.195759.1456ENFazalHayatSchool of Mathematical Sciences, South China Normal University,
Guangzhou 510631, PR ChinaJournal Article20190725The generalized atom-bond connectivity index of a graph <em>G</em> is denoted by ABC<em><sub>a</sub></em>(G) and defined as the sum of weights ((d(u)+d(v)-2)/d(u)d(v))<sup><em><sub>a</sub></em></sup>a$ 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 ABC<em><sub>a</sub></em> 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.https://ijmc.kashanu.ac.ir/article_102513_935bc1ec217d14c2928b98f54b69e2c5.pdf