TY - JOUR
ID - 106057
TI - On the M-polynomial of planar chemical graphs
JO - Iranian Journal of Mathematical Chemistry
JA - IJMC
LA - en
SN - 2228-6489
AU - Deutsch, Emeric
AU - Klavžar, Sandi
AD - Polytechnic Institute of New York University (retired)
AD - Faculty of Mathematics and Physics, University of Ljubljana, Slovenia
Y1 - 2020
PY - 2020
VL - 11
IS - 2
SP - 65
EP - 71
KW - Graph polynomial
KW - Degree-based topological index
KW - planar graph
DO - 10.22052/ijmc.2020.224280.1492
N2 - Let $G$ be a graph and let $m_{i,j}(G)$, $i,jge 1$, be the number of edges $uv$ of $G$ such that ${d_v(G), d_u(G)} = {i,j}$. The $M$-polynomial of $G$ is $M(G;x,y) = sum_{ile j} m_{i,j}(G)x^iy^j$. With $M(G;x,y)$ in hands, numerous degree-based topological indices of $G$ can be routinely computed. In this note a formula for the $M$-polynomial of planar (chemical) graphs which have only vertices of degrees $2$ and $3$ is given that involves only invariants related to the degree $2$ vertices and the number of faces. The approach is applied on several families of chemical graphs. In one of these families an error from the literature is corrected.
UR - https://ijmc.kashanu.ac.ir/article_106057.html
L1 - https://ijmc.kashanu.ac.ir/article_106057_81375683c320f653c28092d0868d56fb.pdf
ER -