Results 11 to 20 of about 29 (29)
On the Harary Estrada index of graphs
Special MatricesLet GG be a connected graph with nn vertices v1,…,vn{v}_{1},\ldots ,{v}_{n}. The Harary matrix of GG, denoted by H(G)H\left(G), is an n×nn\times n matrix with a zero main diagonal, where the (i,j)\left(i,j)-entry is 1d(vi,vj)\frac{1}{d\left({v}_{i},{v}_ ...
Oboudi Mohammad Reza
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Journal of Mathematics, Volume 2025, Issue 1, 2025.In graph theory, the Randic index (R) is a topological graph invariant widely used as a physicochemical descriptor in the mathematical modeling of molecular structures. However, traditional molecular graphs fail to capture the heterogeneity of chemical bonds, since they treat all edges as uniform, ignoring variations in bond lengths and strengths.
Ying Wang +5 more
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Main Group Metal ChemistrySilane compounds are a class of chemical compounds composed of silicon (Si) and hydrogen (H), characterized by the general formula SiH4−xRx{{\rm{SiH}}}_{4-x}{R}_{x}, where RR represents various organic groups. The simplest member of this family is silane
Zhang Xiujun +4 more
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On General Sum‐Connectivity Index and Number of Segments of Fixed‐Order Chemical Trees
Journal of Mathematics, Volume 2025, Issue 1, 2025.Nowadays, one of the most active areas in mathematical chemistry is the study of the mathematical characteristics associated with molecular descriptors. The primary objective of the current study is to find the largest value of χα of graphs in the class of all fixed‐order chemical trees with a particular number of segments for α > 1, where χα is the ...
Muzamil Hanif +5 more
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Journal of Mathematics, Volume 2025, Issue 1, 2025.The multiplicative sum Zagreb index of a graph G is defined as the product of the sum of the degrees of adjacent vertices of G. A molecular tree is an acyclic connected graph with maximum degree at most 4. A vertex in a molecular tree with degree 3 or 4 is referred to as a branching vertex. In this paper, we consider the class of all molecular trees of
Sadia Noureen +6 more
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Main Group Metal ChemistryFor a graph Q=(V,E){\mathbb{Q}}=\left({\mathbb{V}},{\mathbb{E}}), the transformation graph are defined as graphs with vertex set being V(Q)∪E(Q){\mathbb{V}}\left({\mathbb{Q}})\cup {\mathbb{E}}\left({\mathbb{Q}}) and edge set is described following ...
Ali Parvez +5 more
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The minimum exponential atom-bond connectivity energy of trees
Special MatricesLet G=(V(G),E(G))G=\left(V\left(G),E\left(G)) be a graph of order nn. The exponential atom-bond connectivity matrix AeABC(G){A}_{{e}^{{\rm{ABC}}}}\left(G) of GG is an n×nn\times n matrix whose (i,j)\left(i,j)-entry is equal to ed(vi)+d(vj)−2d(vi)d(vj){e}^
Gao Wei
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On the maximum atom-bond sum-connectivity index of molecular trees
AKCE International Journal of Graphs and CombinatoricsLet G be a graph with V(G) and E(G), as vertex set and edge set, respectively. The atom-bond sum-connectivity (ABS) index is a vertex-based topological index which is defined as [Formula: see text] where [Formula: see text] is the degree of the vertex a.
Zhonglin Cheng +2 more
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On the spectral radius and energy of the degree distance matrix of a connected graph
Open MathematicsLet GG be a simple connected graph on nn vertices. The degree of a vertex v∈V(G)v\in V\left(G), denoted by dv{d}_{v}, is the number of edges incident with vv and the distance between any two vertices u,v∈V(G)u,v\in V\left(G), denoted by duv{d}_{uv}, is ...
Khan Zia Ullah, Hameed Abdul
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New bounds on Zagreb connection indices for trees with fixed domination number
AKCE International Journal of Graphs and CombinatoricsA set D of vertices in a graph G is a dominating set of G if every vertex not in D is adjacent to a vertex in D. The domination number, [Formula: see text], is the minimum cardinality among all dominating sets of G.
H. Rahbani +2 more
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