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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Ramanujan Cayley graphs on sporadic groups
(Shahid Rajaee Teacher Training University, 2023-12-01)Let $\Gamma$ be a $k-$regular graph with the second maximum eigenvalue $\lambda$. Then $\Gamma$ is said o be Ramanujan graph if $\lambda\leq 2\sqrt{k-1}.$ Let $G$ be a finite group and $\Gamma=Cay(G,S)$ be a Cayley graph ...
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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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Vertex weighted Laplacian graph energy and other topological indices
(Shahid Rajaee Teacher Training University, 2023-12-01)Let $G$ be a graph with a vertex weight $omega$ and the vertices $v_1,ldots,v_n$. The Laplacian matrix of $G$ with respect to $omega$ is defined as $L_omega(G)=diag(omega(v_1),cdots,omega(v_n))-A(G)$, where $A(G)$ is the ...
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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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Eccentricity Based Indices for Some Classes Fence Graphs
(Shahid Rajaee Teacher Training University, 2023-09-01)One of the most important ideas employed in chemical graph theory is that of so-called topologicalindices. This is to associate a numerical value with a graph structure that often has some kind ofcorrelation with corresponding ...
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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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Edge version of some degree based topological descriptors of graphs
(Shahid Rajaee Teacher Training University, 2023-07-01)In this paper, we study the edge version of some degree based topological indices such as general sum-connectivity index, Randic index, inverse sum indeg index, symmetric division deg index, augmenting Zagreb index and ...
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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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Spectral properties of fullerene graphs
(Shahid Rajaee Teacher Training University, 2018-12-01)Fullerenes are polyhedral molecules made of carbon atoms. These graphs have attracted much attention in the chemical and the mathematical literature. In the present paper, we investigate problems concerned with the eigenvalues ...
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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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Ramanujan Cayley graphs on sporadic groups
(Shahid Rajaee Teacher Training University, 2023-09-01)Let $\Gamma$ be a $k-$regular graph with the second maximum eigenvalue $\lambda$. Then $\Gamma$ is said o be Ramanujan graph if $\lambda\leq 2\sqrt{k-1}.$ Let $G$ be a finite group and $\Gamma=Cay(G,S)$ be a Cayley graph ...
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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, 2023-09-01)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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The adjacency matrix of some hexagonal systems
(Shahid Rajaee Teacher Training University, 2023-09-01)The adjacency matrix is important invariant of a graph with a chemical meaning, when we study the chemical graphs. In this paper, the general form of the adjacency matrices of some hexagonal systems will be determined.
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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 ...
