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The Subset-Strong Product of Graphs
Annales Mathematicae SilesianaeIn this paper, we introduce the subset-strong product of graphs and give a method for calculating the adjacency spectrum of this product. In addition, exact expressions for the first and second Zagreb indices of the subset-strong products of two graphs ...
Eliasi Mehdi
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Gromov hyperbolicity in strong product graphs [PDF]
The Electronic Journal of Combinatorics, 2013 If X is a geodesic metric space and x1; x2; x3 2 X, a geodesic triangle T = fx1; x2; x3g is the union of the three geodesics [x1x2], [x2x3] and [x3x1] in X.
Carballosa, Walter +3 more
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On the strong metric dimension of the strong products of graphs
Open Mathematics, 2015 Let G be a connected graph. A vertex w ∈ V.G/ strongly resolves two vertices u,v ∈ V.G/ if there exists some shortest u-w path containing v or some shortest v-w path containing u.
Kuziak Dorota +2 more
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Bounding the Open k-Monopoly Number of Strong Product Graphs
Discussiones Mathematicae Graph Theory, 2018 Let G = (V, E) be a simple graph without isolated vertices and minimum degree δ, and let k ∈ {1 − ⌈δ/2⌉, . . . , ⌊δ/2⌋} be an integer. Given a set M ⊂ V, a vertex v of G is said to be k-controlled by M if δM(v)≥δG(v)2+k$\delta _M (v) \ge {{\delta _G (v)}
Kuziak Dorota +2 more
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Connectivity of Strong Products of Graphs [PDF]
Graphs and Combinatorics, 2010 The strong product of graphs is one of the three commutative and associative graph products. Let \(S\) be the strong product of two given graphs. The author proves that every minimum separating set in \(S\) is either an \(I\)-set or an \(L\)-set in \(S\).
Ladinek, Irena Hrastnik, Spacapan, Simon
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Strong Edge Coloring of Cayley Graphs and Some Product Graphs [PDF]
Graphs and Combinatorics, 2022 AbstractA strong edge coloring of a graph G is a proper edge coloring of G such that every color class is an induced matching. The minimum number of colors required is termed the strong chromatic index. In this paper we determine the exact value of the strong chromatic index of all unitary Cayley graphs.
Suresh Dara +3 more
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Strong chromatic index of products of graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2007 The strong chromatic index of a graph is the minimum number of colours needed to colour the edges in such a way that each colour class is an induced matching.
Olivier Togni
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Hamiltonian Cycles in Strong Products of Graphs [PDF]
Canadian Mathematical Bulletin, 1979 Abstract. Let denote the graph (k times) where is the strong product of the two graphs G and H. In this paper we prove the conjecture of J. Zaks [3]: For every connected graph G with at least two vertices there exists an integer k = k(G) for which the graph is hamiltonian.
Bermond, J. C. +2 more
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Roman domination in Cartesian product graphs and strong product graphs [PDF]
Applicable Analysis and Discrete Mathematics, 2013 A map f : V ? {0, 1, 2} is a Roman dominating function for G if for every vertex v with f(v) = 0, there exists a vertex u, adjacent to v, with f(u) = 2. The weight of a Roman dominating function is f(V ) = ?u?v f(u). The minimum weight of a Roman dominating function on G is the Roman domination number of G.
Yero, Ismael G. +1 more
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Bounds on the Twin-Width of Product Graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2023 Twin-width is a graph width parameter recently introduced by Bonnet, Kim, Thomass\'{e} & Watrigant. Given two graphs $G$ and $H$ and a graph product $\star$, we address the question: is the twin-width of $G\star H$ bounded by a function of the twin ...
William Pettersson, John Sylvester
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