Results 51 to 60 of about 131 (96)
On the multiplicative sum Zagreb index of molecular graphs
Open MathematicsMultiplicative sum Zagreb index is a modified version of the famous Zagreb indices. For a graph GG, the multiplicative sum Zagreb index is defined as Π1*(G)=∏uv∈E(G)(dG(u)+dG(v)){\Pi }_{1}^{* }\left(G)={\prod }_{uv\in E\left(G)}\left({d}_{G}\left(u)+{d}_{
Sun Xiaoling, Du Jianwei, Mei Yinzhen
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Trees with Unique Least Central Subtrees
Discussiones Mathematicae Graph Theory, 2018 A subtree S of a tree T is a central subtree of T if S has the minimum eccentricity in the join-semilattice of all subtrees of T. Among all subtrees lying in the join-semilattice center, the subtree with minimal size is called the least central subtree ...
Kang Liying, Shan Erfang
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A Note on the Interval Function of a Disconnected Graph
Discussiones Mathematicae Graph Theory, 2018 In this note we extend the Mulder-Nebeský characterization of the interval function of a connected graph to the disconnected case. One axiom needs to be adapted, but also a new axiom is needed in addition.
Changat Manoj +3 more
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On the sandpile model of modified wheels II
Open Mathematics, 2020 We investigate the abelian sandpile group on modified wheels Wˆn{\hat{W}}_{n} by using a variant of the dollar game as described in [N. L. Biggs, Chip-Firing and the critical group of a graph, J. Algebr. Comb. 9 (1999), 25–45].
Raza Zahid +3 more
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The Minimum Size of a Graph with Given Tree Connectivity
Discussiones Mathematicae Graph Theory, 2021 For a graph G = (V, E) and a set S ⊆ V of at least two vertices, an S-tree is a such subgraph T of G that is a tree with S ⊆ V (T). Two S-trees T1 and T2 are said to be internally disjoint if E(T1) ∩ E(T2) = ∅ and V (T1) ∩ V (T2) = S, and edge-disjoint ...
Sun Yuefang, Sheng Bin, Jin Zemin
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Domination Subdivision and Domination Multisubdivision Numbers of Graphs
Discussiones Mathematicae Graph Theory, 2019 The domination subdivision number sd(G) of a graph G is the minimum number of edges that must be subdivided (where an edge can be subdivided at most once) in order to increase the domination number of G. It has been shown [10] that sd(T) ≤ 3 for any tree
Dettlaff Magda +2 more
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Inverse Problem on the Steiner Wiener Index
Discussiones Mathematicae Graph Theory, 2018 The Wiener index W(G) of a connected graph G, introduced by Wiener in 1947, is defined as W(G) =∑u,v∈V (G)dG(u, v), where dG(u, v) is the distance (the length a shortest path) between the vertices u and v in G. For S ⊆ V (G), the Steiner distance d(S) of
Li Xueliang, Mao Yaping, Gutman Ivan
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Some remarks on the Dirichlet problem on infinite trees
Concrete Operators, 2019 We consider the Dirichlet problem on in_nite and locally _nite rooted trees, andwe prove that the set of irregular points for continuous data has zero capacity. We also give some uniqueness results for solutions in Sobolev W1,p of the tree.
Chalmoukis Nikolaos, Levi Matteo
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A formula for all minors of the adjacency matrix and an application
Special Matrices, 2014 We supply a combinatorial description of any minor of the adjacency matrix of a graph. This descriptionis then used to give a formula for the determinant and inverse of the adjacency matrix, A(G), of agraph G, whenever A(G) is invertible, where G is ...
Bapat R. B., Lal A. K., Pati S.
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Exact solutions and bounds for network SIR and SEIR models using a rooted-tree approximation. [PDF]
J Math Biol, 2023 Hall CL, Siebert BA.
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