Results 1 to 10 of about 187 (132)
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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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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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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Discussiones Mathematicae Graph Theory, 2021 In this paper, we study a new distance parameter triameter of a connected graph G, which is defined as max{d(u; v)+d(v;w)+d(u;w) : u; v;w ∈ V }and is denoted by tr(G).
Das Angsuman
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Some improved bounds on two energy-like invariants of some derived graphs
Open Mathematics, 2019 Given a simple graph G, its Laplacian-energy-like invariant LEL(G) and incidence energy IE(G) are the sum of square root of its all Laplacian eigenvalues and signless Laplacian eigenvalues, respectively. This paper obtains some improved bounds on LEL and
Cui Shu-Yu, Tian Gui-Xian
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