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Note on strong product graph dimension
The Art of Discrete and Applied Mathematics, 2023Summary: In this paper we define a new dimension of graphs based on the strong product. Strong product can be viewed as a categorical product in a modified category. Unlike in the standard case where the system of basic generators (``simplest objects'') is very transparent but necessarily infinite, we have here a single generator.
Nešetřil, Jaroslav, Pultr, Aleš
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Tensor products and strong products of soft graphs
Discrete Mathematics, Algorithms and Applications, 2022Molodtsov developed soft set theory in 1999 as an approach for modeling vagueness and uncertainty. Many academics currently employ soft set theory to solve decision-making problems. A parameterized point of view for graphs is provided using the idea of soft graphs.
Bobin George +2 more
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Pancyclicity of Strong Products of Graphs
Graphs and Combinatorics, 2004A graph with \(n\) vertices is pancyclic if it contains a cycle of length \(s\) for all \(s\), \(3\leq s\leq n\). In particular, a pancyclic graph is Hamiltonian. The {strong product} of \(k\) graphs \(G_1=(V_1,E_1),\dots, G_k=(V_k,E_k)\) is the graph \(G_1\times\cdots\times G_k\) with \(V_1\times\cdots \times V_k\) as set of vertices and two vertices \
Král, Daniel +3 more
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Strong product of factor-critical graphs
International Journal of Computer Mathematics, 2011Strong product G1⊠ G2 of two graphs G1 and G2 has a vertex set V(G1)×V(G2) and two vertices (u1, v1) and (u2, v2) are adjacent whenever u1=u2 and v1 is adjacent to v2 or u1 is adjacent to u2 and v1=v2, or u1 is adjacent to u2 and v1 is adjacent to v2. We investigate the factor-criticality of G1⊠ G2 and obtain the following. Let G1 and G2 be connected m-
Zefang Wu, Xu Yang, Qinglin Yu
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Game chromatic number of strong product graphs
Discrete Mathematics, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hikoe Enomoto +2 more
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Hamilton cycles in strong products of graphs
Journal of Graph Theory, 2005AbstractWe prove that the strong product of any n connected graphs of maximum degree at most n contains a Hamilton cycle. In particular, GΔ(G) is hamiltonian for each connected graph G, which answers in affirmative a conjecture of Bermond, Germa, and Heydemann. © 2005 Wiley Periodicals, Inc.
Král', Daniel +3 more
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Super Edge-Connectivity of Strong Product Graphs
Journal of Interconnection Networks, 2017The super edge-connectivity [Formula: see text] of a connected graph G is the minimum cardinality of an edge-cut F in G such that every component of G − F contains at least two vertices. Denote by [Formula: see text] the strong product of graphs G and H. For two graphs G and H, Yang proved that [Formula: see text]. In this paper, we give another proof
ZHAO WANG +3 more
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The differential of the strong product graphs
International Journal of Computer Mathematics, 2014Let G=(V, E) be a graph of order n and let B(D) be the set of vertices in V ∖ D that have a neighbour in the set D. The differential of a set D is defined as ∂ (D)=|B(D)|−|D| and the differential of a graph to equal the maximum value of ∂(D) for any subset D of V.
S. Bermudo +3 more
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