TY - JOUR
ID - 111292
TI - Computing the Mostar Index in Networks with Applications to Molecular Graphs
JO - Iranian Journal of Mathematical Chemistry
JA - IJMC
LA - en
SN - 2228-6489
AU - Tratnik, Niko
AD - University of Maribor, Faculty of Natural Sciences and Mathematics
Y1 - 2021
PY - 2021
VL - 12
IS - 1
SP - 1
EP - 18
KW - Mostar index
KW - cut method
KW - Weighted graph
KW - tree-like polyphenyl system
KW - benzenoid system
DO - 10.22052/ijmc.2020.240316.1526
N2 - Recently, a bond-additive topological descriptor, named as the Mostar index, has been introduced as a measure of peripherality in networks. For a connected graph $G$, the Mostar index is defined as $Mo(G) = \sum_{e=uv \in E(G)} |n_u(e) - n_v(e)|$, where for an edge $e=uv$ we denote by $n_u(e)$ the number of vertices of $G$ that are closer to $u$ than to $v$ and by $n_v(e)$ the number of vertices of $G$ that are closer to $v$ than to $u$. In the present paper, we prove that the Mostar index of a weighted graph can be computed in terms of Mostar indices of weighted quotient graphs. Inspired by this result, several generalizations to other versions of the Mostar index already appeared in the literature. Furthermore, we apply the obtained method to benzenoid systems, tree-like polyphenyl systems, and to a fullerene patch. Closed-form formulas for two families of these molecular graphs are also deduced.
UR - https://ijmc.kashanu.ac.ir/article_111292.html
L1 - https://ijmc.kashanu.ac.ir/article_111292_97ff81ab88f1726ca8516ec53cdfe05e.pdf
ER -