Title of article :
On the M-polynomial of Planar Chemical Graphs
Author/Authors :
DEUTSCH, EMERIC Polytechnic Institute of New York University - United States , KLAVŽAR, SANDI Faculty of Mathematics and Physics - University of Ljubljana - Slovenia - Institute of Mathematics - Physics and Mechanics - Ljubljana - Slovenia - Faculty of Natural Sciences and Mathematics - University of Maribor - Slovenia
Abstract :
Let ܩbe a graph and let ݉( ≥ ݆ ,݅ ,)ܩ1, be the number of edges ݒݑ
of ܩsuch that {݀௩(G), ݀௨( .}݆ ,݅{ = })ܩThe -ܯpolynomial of ܩis
∑ = )ݕ ,ݔ ;ܩ(ܯஸ( .ݔ)ܩWith )ݕ ,ݔ ;ܩ(ܯin hands, numerous
degree-based topological indices of ܩcan be routinely computed. In
this note a formula for the -ܯpolynomial 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.
Keywords :
M-polynomial , Degree-based topological index , Planar graph
Journal title :
Iranian Journal of Mathematical Chemistry
