TY - JOUR
ID - 102513
TI - On Generalized Atom-bond Connectivity Index of Cacti
JO - Iranian Journal of Mathematical Chemistry
JA - IJMC
LA - en
SN - 2228-6489
AU - Hayat, Fazal
AD - School of Mathematical Sciences, South China Normal University,
Guangzhou 510631, PR China
Y1 - 2019
PY - 2019
VL - 10
IS - 4
SP - 319
EP - 330
KW - Atom-bond connectivity index
KW - Cactus
KW - Extremal graph
KW - Pendant vertices
DO - 10.22052/ijmc.2019.195759.1456
N2 - 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.
UR - https://ijmc.kashanu.ac.ir/article_102513.html
L1 - https://ijmc.kashanu.ac.ir/article_102513_935bc1ec217d14c2928b98f54b69e2c5.pdf
ER -