Results 61 to 70 of about 1,362 (112)
A Constructive Characterization of Vertex Cover Roman Trees
Discussiones Mathematicae Graph Theory, 2021 A Roman dominating function on a graph G = (V (G), E(G)) is a function f : V (G) → {0, 1, 2} satisfying the condition that every vertex u for which f (u) = 0 is adjacent to at least one vertex v for which f (v) = 2.
Martínez Abel Cabrera +2 more
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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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Independent Transversal Total Domination Versus Total Domination in Trees
Discussiones Mathematicae Graph Theory, 2021 A subset of vertices in a graph G is a total dominating set if every vertex in G is adjacent to at least one vertex in this subset. The total domination number of G is the minimum cardinality of any total dominating set in G and is denoted by γt(G).
Martínez Abel Cabrera +2 more
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The Product Connectivity Banhatti Index of A Graph
Discussiones Mathematicae Graph Theory, 2019 Let G = (V, E) be a connected graph with vertex set V (G) and edge set E(G). The product connectivity Banhatti index of a graph G is defined as, PB(G)=∑ue1dG(u)dG(e)$PB(G) = \sum\nolimits_{ue} {{1 \over {\sqrt {{d_G}(u){d_G}(e)} }}}$ where ue means that ...
Kulli V.R. +2 more
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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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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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Open Mathematics, 2016 As a generalization of the Sierpiński-like graphs, the subdivided-line graph Г(G) of a simple connected graph G is defined to be the line graph of the barycentric subdivision of G.
Shang Yilun
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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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