Results 1 to 10 of about 1,105 (94)
Steiner distance matrix of caterpillar graphs
Special Matrices, 2022 In this article, we show that the rank of the 2-Steiner distance matrix of a caterpillar graph having NN vertices and pp pendant veritices is 2N−p−12N-p-1.
Azimi Ali +2 more
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Graphs that are Critical for the Packing Chromatic Number
Discussiones Mathematicae Graph Theory, 2022 Given a graph G, a coloring c : V (G) → {1, …, k} such that c(u) = c(v) = i implies that vertices u and v are at distance greater than i, is called a packing coloring of G.
Brešar Boštjan, Ferme Jasmina
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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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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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Spectral Conditions for Graphs to be k-Hamiltonian or k-Path-Coverable
Discussiones Mathematicae Graph Theory, 2020 A graph G is k-Hamiltonian if for all X ⊂ V (G) with |X| ≤ k, the subgraph induced by V (G) \ X is Hamiltonian. A graph G is k-path-coverable if V (G) can be covered by k or fewer vertex disjoint paths.
Liu Weijun +3 more
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On the general position number of two classes of graphs
Open Mathematics, 2022 The general position problem is to find the cardinality of the largest vertex subset SS such that no triple of vertices of SS lies on a common geodesic.
Yao Yan, He Mengya, Ji Shengjin
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On Antipodal and Diametrical Partial Cubes
Discussiones Mathematicae Graph Theory, 2021 We prove that any diametrical partial cube of diameter at most 6 is antipodal. Because any antipodal graph is harmonic, this gives a partial answer to a question of Fukuda and Handa [Antipodal graphs and oriented matroids, Discrete Math.
Polat Norbert
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Independence Number and Packing Coloring of Generalized Mycielski Graphs
Discussiones Mathematicae Graph Theory, 2021 For a positive integer k ⩾ 1, a graph G with vertex set V is said to be k-packing colorable if there exists a mapping f : V ↦ {1, 2, . . ., k} such that any two distinct vertices x and y with the same color f(x) = f(y) are at distance at least f(x) + 1 ...
Bidine Ez Zobair +2 more
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