Results 21 to 30 of about 1,116 (99)
An O(mn2) Algorithm for Computing the Strong Geodetic Number in Outerplanar Graphs
Discussiones Mathematicae Graph Theory, 2022 Let G = (V (G), E(G)) be a graph and S be a subset of vertices of G. Let us denote by γ[u, v] a geodesic between u and v. Let Γ(S) = {γ[vi, vj] | vi, vj ∈ S} be a set of exactly |S|(|S|−1)/2 geodesics, one for each pair of distinct vertices in S.
Mezzini Mauro
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On the diameter of the Kronecker product graph [PDF]
, 2012 Let $G_1$ and $G_2$ be two undirected nontrivial graphs. The Kronecker product of $G_1$ and $G_2$ denoted by $G_1\otimes G_2$ with vertex set $V(G_1)\times V(G_2)$, two vertices $x_1x_2$ and $y_1y_2$ are adjacent if and only if $(x_1,y_1)\in E(G_1)$ and $
Hu, Fu-Tao, Xu, Jun-Ming
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Computing the Metric Dimension of a Graph from Primary Subgraphs
Discussiones Mathematicae Graph Theory, 2017 Let G be a connected graph. Given an ordered set W = {w1, . . . , wk} ⊆ V (G) and a vertex u ∈ V (G), the representation of u with respect to W is the ordered k-tuple (d(u, w1), d(u, w2), . . .
Kuziak Dorota +2 more
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The second out-neighborhood for local tournaments
Open Mathematics, 2020 Sullivan stated the conjectures: (1) every oriented graph has a vertex x such that d ++(x) ≥ d −(x) and (2) every oriented graph has a vertex x such that d ++(x) + d +(x) ≥ 2d −(x)
Li Ruijuan, Liang Juanjuan
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Further new results on strong resolving partitions for graphs
Open Mathematics, 2020 A set W of vertices of a connected graph G strongly resolves two different vertices x, y ∉ W if either d G(x, W) = d G(x, y) + d G(y, W) or d G(y, W) = d G(y, x) + d
Kuziak Dorota, Yero Ismael G.
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The Threshold Dimension and Irreducible Graphs
Discussiones Mathematicae Graph Theory, 2023 Let G be a graph, and let u, v, and w be vertices of G. If the distance between u and w does not equal the distance between v and w, then w is said to resolve u and v.
Mol Lucas +2 more
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Proximity, remoteness and maximum degree in graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2022 The average distance of a vertex $v$ of a connected graph $G$ is the arithmetic mean of the distances from $v$ to all other vertices of $G$. The proximity $\pi(G)$ and the remoteness $\rho(G)$ of $G$ are the minimum and the maximum of the average ...
Peter Dankelmann +2 more
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Hyper-Wiener indices of polyphenyl chains and polyphenyl spiders
Open Mathematics, 2019 Let G be a connected graph and u and v two vertices of G. The hyper-Wiener index of graph G is WW(G)=12∑u,v∈V(G)(dG(u,v)+dG2(u,v))$\begin{array}{} WW(G)=\frac{1}{2}\sum\limits_{u,v\in V(G)}(d_{G}(u,v)+d^{2}_{G}(u,v)) \end{array}$, where dG(u, v) is the ...
Wu Tingzeng, Lü Huazhong
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The mixed metric dimension of flower snarks and wheels
Open Mathematics, 2021 New graph invariant, which is called a mixed metric dimension, has been recently introduced. In this paper, exact results of the mixed metric dimension on two special classes of graphs are found: flower snarks Jn{J}_{n} and wheels Wn{W}_{n}. It is proved
Danas Milica Milivojević
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Power graphs and exchange property for resolving sets
Open Mathematics, 2019 Classical applications of resolving sets and metric dimension can be observed in robot navigation, networking and pharmacy. In the present article, a formula for computing the metric dimension of a simple graph wihtout singleton twins is given.
Abbas Ghulam +4 more
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