Iranian Journal of Mathematical Chemistry
Volume:12 Issue: 4, Autumn 2021

Recently, a novel topological index, Sombor index, was introduced by Gutman, defined as $SO(G)=sumlimits_{uvin E(G)}sqrt{d_{u}^{2}+d_{v}^{2}}$, where $d_{u}$ denotes the degree of vertex $u$. In this paper, we first determine the maximum Sombor index among cacti with $n$ vertices and $t$ cycles, then determine the maximum Sombor index among cacti with perfect matchings. We also characterize corresponding maximum cacti.

Gutman recently introduced a new vertex-degree-based topological index called the Sombor index. In this paper, we present some new results relating the Sombor index and some well-studied topological indices: Zagreb indices, forgotten index, harmonic index, (general) sum-connectivity index and symmetric division deg index.

Altans are a class of molecular graphs introduced recently. These graphs are attractive to many chemists and mathematicians. A topological index is a numerical invariant calculated for a description of molecular graphs. In this paper, we compute a few topological indices of Altans such as Wiener index, second Zagreb index, atom-bond connectivity (ABC) index, 〖ABC〗_4 index, etc.

Randi{'c} index belongs to the most well-known topological indices in chemical graph theory. In this paper, we find upper bound for the Randi{'c} index of trees in terms of the order and the total domination number. The extremal trees are characterized.

‎‎In this paper‎, ‎the radial basis functions (RBFs) method is applied to solve the coupled Lane–Emden boundary value problems arising in catalytic diffusion reactions‎. ‎First‎, ‎we multiply the equations by x to overcome the difficulties of the singularity at the origin‎. ‎Then‎, ‎the Kansa collocation method based on radial basis functions is used to approximate the unknown functions‎. ‎By this technique‎, ‎the problem with boundary conditions is reduced to a system of algebraic equations‎. ‎We solve this system and compare the maximal residual error with the results previously‎, ‎which show the presented method is efficient and produces very accurate and rapidly convergent numerical results in considerably low computational effort and easy implementation‎.