Iranian Journal of Mathematical Chemistry
https://ijmc.kashanu.ac.ir/
Iranian Journal of Mathematical Chemistryendaily1Wed, 01 Mar 2023 00:00:00 +0330Wed, 01 Mar 2023 00:00:00 +0330In Memory of Professor Ali Reza Ashrafi (1964-2023): A Matchless Role Model in Mathematical Chemistry in Iran
https://ijmc.kashanu.ac.ir/article_113781.html
&lrm;On the Number of Perfect Star Packing and Perfect Pseudo Matching in Some Fullerene Graphs
https://ijmc.kashanu.ac.ir/article_113782.html
A perfect star packing in a fullerene graph G is a spanning subgraph of G whose every component is isomorphic to the star graph K_1,3. A perfect pseudo matching of a fullerene graph G is a spanning subgraph H of G such that each component of H is either K_2 or K_1,3. In this paper, we examine the number of perfect star packing in (3,6)-fullerene graphs and perfect pseudo matching in chamfered fullerene graphs.On General Degree-Eccentricity Index For Trees with Fixed Diameter and Number of Pendent Vertices
https://ijmc.kashanu.ac.ir/article_113783.html
The general degree-eccentricity index of a graph $G$ is defined by,$DEI_{a,b} (G) = \sum_{v \in V(G)} d_{G}^{a}(v) ecc_{G}^{b}(v)$ for $a, b \in \mathbb{R}$, where $V(G)$ is the vertex set of $G$, $ecc_{G}(v)$ is the eccentricity of a vertex $v$ and $d_{G}(v)$ is the degree of $v$ in $G$.In this paper, we generalize results on the general eccentric connectivity index fortrees.We present upper and lower bounds on the general degree-eccentricity index for trees of given order and diameter, and trees of given order and number of pendant vertices.The upper bounds hold for $a &gt; 1$ and $b \in \mathbb{R}\setminus\{0\}$ andthe lower bounds holds for $0 &lt; a &lt; 1$ and $b \in \mathbb{R}\setminus\{0\}$.We include the case $a = 1$ and $b \in \{-1, 1\}$ in those theorems for which the proof of that case is not complicated.We present all the extremal graphs, which means that our bounds are best possible.Entire Sombor Index of Graphs
https://ijmc.kashanu.ac.ir/article_113784.html
Let $G=(V, E)$ be a simple graph with vertex set $V$ and edge set $E$. The Sombor index of the graph $G$ is a degree-based topological index, defined as$$SO(G)=\sum_{uv \in E}\sqrt{d(u)^2+d(v)^2},$$in which $d(x)$ is the degree of the vertex $x \in V$ for $x=u, v$. \\In this paper, we introduce a new topological index called the entire Sombor index of a graph which is defined as the sum of the terms $\sqrt{d(x)^2+d(y)^2}$ where $x$ is either adjacent or incident to $y$ and $x, y \in V \cup E$. We obtain exact values of this new topological index in some graphs families. Some important properties of this index are obtained.Edge Metric Dimension of Fullerenes
https://ijmc.kashanu.ac.ir/article_113785.html
&lrm;A $(k,6)$-fullerene graph is a planar $3$-connected cubic graph whose faces are $k$-gons and hexagons&lrm;. &lrm;The aim of this paper is to&lrm; study the edge metric dimension of $(3,6)$&lrm;- &lrm;and $(4,6)$-fullerene graphs&lrm;.Spectral Poly-Sinc Collocation Method for Solving a Singular Nonlinear BVP of Reaction-Diffusion with Michaelis-Menten Kinetics in a Catalyst/Biocatalyst
https://ijmc.kashanu.ac.ir/article_113737.html
In this paper we revisit a nonlinear singular boundary value problem (SBVP) which arises frequently in mathematical model of diffusion and reaction in porous catalysts or biocatalyst pellets. A new simple variant of sinc methods so-called poly-sinc collocation method, is presented to solve non-isothermal reaction-diffusion model equation in a spherical catalyst and reaction-diffusion model equation in an electroactive polymer film. This method reduces each problem into a system of nonlinear algebraic equations, and on solving them by Newton's iteration method, we obtain the approximate solution. Through testing with numerical examples, it is found that our technique has exponentially decaying error property and performs well near singularity like other conventional sinc methods. The obtained results are in good agreement with previously reported results in the literature, and there is an impressive degree of agreement between our results and those obtained by a MAPLE ODE solver. Furthermore, the high accuracy of method is verified by using a residual evaluation strategy.