Journal of Mathematical Nanoscience
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Computing two types of geometric-arithmetic indices of some benzenoid graphs
(Shahid Rajaee Teacher Training University, 2023-09-01)The geometric-arithmetic index is a topological index was defined as $GA(G)=\sum{uv\in E(G)}\frac{2\sqrt{d_ud_v}}{d_u+d_v}}$, where du denotes the degree of vertex u in G. By replacing instead $\delta_u=\sum_{v\cong u} ...
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ON PAIRS OF NON-ABELIAN FINITE P-GROUPS
(Shahid Rajaee Teacher Training University, 2023-12-01)Let (N;G) be a pair of non-abelian finite p-groups and K be anormal subgroup of G such that G = N \times K, where K is a d-generator groupof order pm. Moreover, let |N| = p^n and {N'| = p^k. Then |M(N;G)|=p^{1/2 ...
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On the conjecture for the sum of the largest signless Laplacian eigenvalues of a graph- a survey
(Shahid Rajaee Teacher Training University, 2023-12-01)Let $G$ be a simple graph with order $n$ and size $m$. Let $D(G)=$ diag$(d_1, d_2, \dots, d_n)$ be its diagonal matrix, where $d_i=\deg(v_i),$ for all $i=1,2,\dots,n$ and $A(G)$ be its adjacency matrix. The matrix ...
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Computing Degree-Based Topological Indices of Polyhex Nanotubes
(Shahid Rajaee Teacher Training University, 2023-12-01)Recently, Shigehalli and Kanabur [20] have put forward for new degree based topological indices, namely Arithmetic-Geometric index (AG1 index), SK index, SK1 index and SK2 index of a molecular graph G. In this paper, we ...
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Eyes on the cosmic web: A tribute to Ali Reza Ashrafi
(Shahid Rajaee Teacher Training University, 2023-12-01)This article delves into the subject of topological modeling and invariants in the study of the Cosmic Web (CW), which refers to the vast network of galaxies in the universe. The article explores the use of eccentric ...
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On an interesting hypothesis of the theory of formal languages
(Shahid Rajaee Teacher Training University, 2023-09-01)The formulation of a hypothesis for any pair of nonempty finite languages is considered. The hypothesis consists in the formulation of the necessary conditions for the equality of infinite iterations of these languages, ...
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Energy of graphs
(Shahid Rajaee Teacher Training University, 2023-09-01)The energy, E(G), of a simple graph G is defined to be the sum of the absolute values of the eigen values of G. In this paper, we introduce some in-equalities of energy of graphs.
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A survey on symmetric division degree index
(Shahid Rajaee Teacher Training University, 2018-12-01)The symmetric division degree (SDD) index is one the 148 discrete Adriatic indices,introduced by Vukicevi´c et al. as a remarkable predictor of total surface area of polychlorobiphenyls.The SDD index has already been proved ...
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A generalized version of symmetric division degree index
(Shahid Rajaee Teacher Training University, 2018-06-01)The symmetric division degree $SDD$-index of a simple connected graph $G$ is defined as the sum of terms $f(d_u,d_v)=(d_u/d_v)+(d_v/d_u)$ over all pairs of distinct adjacent vertices of $G$; where $d_u$ denotes the degree ...
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Power graphs via their characteristic polynomial
(Shahid Rajaee Teacher Training University, 2023-09-01)A power graph is defined a graph that it's vertices are the elements of group and two vertices are adjacent if and only if one of them is a power of the other. Suppose $A(X)$ is the adjacency matrix of graph $X$. Then the ...
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Edge deletion and symmetric division degree index of graphs
(Shahid Rajaee Teacher Training University, 2023-09-01)The symmetric division deg index (or simply SDD) was proposed by Vukicevic et al.as a remarkable predictor of total surface area of polychlorobiphenyls. We are interested in how the SDD of a graph changes when edges are ...
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History of Mathematical-Chemistry in Iran: Scientific works of Alireza Ashrafi
(Shahid Rajaee Teacher Training University, 2023-09-01)The field of mathematical chemistry started with the pure and memorable activities of Alireza Ashrafi in Iran. One of the most important factors in the rapid expansion of this branchof science in Iran, which intensified ...
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Tetravalent one-regular graphs of order p2q2
(Shahid Rajaee Teacher Training University, 2023-07-01)A graph is called one-regular if its full automorphism group acts regularly on the set of arcs. In this paper, we classify all connected one-regular graphs of valency 4 of order $p^2q^2$, where $p>q$ are prime numbers. We ...
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On linear combinations between Zagreb indices/coindices of a line graph
(Shahid Rajaee Teacher Training University, 2023-07-01)Let $G=(V,E)$, $V=\left\{ v_{1},v_{2},\ldots ,v_{n}\right\}$, be a simple graph of order $n$ and size $m$.Denote by $\Delta = d_1\ge d_2 \ge \cdots \ge d_n= \delta$, $d_i=d(v_i)$, and $\Delta_e=d(e_1)\ge d(e_2)\ge \cdots ...
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Topological indices of drug molecular structures: An application with the treatment and prevention of Covid-19
(Shahid Rajaee Teacher Training University, 2023-07-01)This paper presents a comprehensive analysis of the role of topological indices andcentrality measures in predicting the chemical properties of molecules, with a specific focus on sixdrugs known for their effectiveness in ...
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On the covering radius of DNA code over a finite ring
(Shahid Rajaee Teacher Training University, 2023-07-01)In this paper, lower bound and upper bound on the covering radius ofDNA codes over a finite ring N with respect to Chinese euclidean distanceare given. Also determine the covering radius of various Repetition DNAcodes, ...
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Automorphism group of quasi-abelian semi-Cayley graphs
(Shahid Rajaee Teacher Training University, 2023-06-01)Let G be a group and R,L,S be subsets of G such that $R=R^{-1}$, $L=L^{-1}$ and $1\notin R\cup L$. The undirected graph $\SC(G;R,L,S)$ with vertex set union of $G_1=\{g_1\mid g\in G\}$ and $G_2=\{g_2\mid g\in G\}$, and ...
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A survey on symmetric division degree index
(Shahid Rajaee Teacher Training University, 2023-07-01)The symmetric division degree (SDD) index is one the 148 discrete Adriatic indices,introduced by Vukicevi´c et al. as a remarkable predictor of total surface area of polychlorobiphenyls.The SDD index has already been proved ...
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The generalized moving least squares technique combined with a Householder transformation for computing the first derivatives on the sphere
(Shahid Rajaee Teacher Training University, 2023-06-01)We present a new and simple direct approach based on generalized moving least squares (GMLS) for computing the first derivatives of the functions defined on the sphere. The novel method utilizes a Householder transformation ...
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Hosoya index of total graphs and semitotal graphs
(Shahid Rajaee Teacher Training University, 2023-06-01)The Hosoya index $Z(G)$ of a graph $G$ is the total number of matchings in it. In this paper, the recursive formulas of the Hosoya index of semitotal graph $Q(G)$ and total graph $T(G)$ for certain graphs $G$ are obtained. ...
