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The Subset-Strong Product of Graphs [PDF]
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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Spectrum and Ricci Curvature on the Weighted Strong Product Graphs [PDF]
IEEE Access, 2023 The strong product on graphs is also called the normal product or the AND product. It is the union of Cartesian product and tensor product, and also is a binary operation on graphs. This operation takes two graphs and produces a new graph. In this paper,
Xiaoxiao Zhang, Zenghui Fang
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Computing FGZ Index of Sum Graphs under Strong Product [PDF]
Journal of Mathematics, 2021 Topological index (TI) is a function that assigns a numeric value to a (molecular) graph that predicts its various physical and structural properties. In this paper, we study the sum graphs (S-sum, R-sum, Q-sum and T-sum) using the subdivision related ...
Zhi-Ba Peng +3 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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Bootstrap percolation in strong products of graphs [PDF]
The Electronic Journal of Combinatorics, 2023 Given a graph $G$ and assuming that some vertices of $G$ are infected, the $r$-neighbor bootstrap percolation rule makes an uninfected vertex $v$ infected if $v$ has at least $r$ infected neighbors. The $r$-percolation number, $m(G,r)$, of $G$ is the minimum cardinality of a set of initially infected vertices in $G$ such that after continuously ...
Boštjan Brešar, Jaka Hedžet
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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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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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The local metric dimension of strong product graphs [PDF]
Graphs and Combinatorics, 2015 A vertex $v\in V(G)$ is said to distinguish two vertices $x,y\in V(G)$ of a nontrivial connected graph $G$ if the distance from $v$ to $x$ is different from the distance from $v$ to $y$. A set $S\subset V(G)$ is a local metric generator for $G$ if every two adjacent vertices of $G$ are distinguished by some vertex of $S$.
Gabriel A. Barragán-Ramírez +1 more
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Strong products ofϰ-critical graphs [PDF]
Aequationes Mathematicae, 1993 LetG[H] be the lexicographic product and letG ⊠H be the strong product of the graphsG andH. It is proved that, ifG is aϰ-critical graph, then, for any graphH, $$\chi (G[H]) \leqslant \chi (H)(\chi (G) - 1) + \left[ {\frac{{\chi (H)}}{{\alpha (G)}}} \right ...
Sandi Klavžar
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Estimation of Laplacian spectra of direct and strong product graphs [PDF]
, 2015 Calculating a product of multiple graphs has been studied in mathematics, engineering, computer science, and more recently in network science, particularly in the context of multilayer networks. One of the important questions to be addressed in this area
Sayama, Hiroki
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