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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 \
Daniel Král +3 more
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Hamiltonian decompositions of strong products
Journal of Graph Theory, 1998Summary: It is shown that if two graphs are Hamiltonian decomposable, then so is their strong product.
Cong Fan, Jiuqiang Liu
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Pancyclicity and extendability in strong products
Journal of Graph Theory, 1996A graph \(G\) is said to be 1-edge Hamiltonian if after the deletion of any edge, the resulting graph is Hamiltonian; \(G\) has pancyclic ordering if its vertices can be labeled \(v_1, v_2,\dots, v_n\) such that the subgraph induced by \(v_1, v_2,\dots, v_k\) contains a cycle of length \(k\) with \(3\leq k\leq n\).
S. Ramachandran, R. Parvathy
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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.
Sergio Bermudo +3 more
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On the Strong Connectedness of the Direct Product
IEEE Transactions on Electronic Computers, 1967A result relating the strong connectedness of a product and the nonexistence of a homomorphism between the factors is given.
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Product Operations in Strong Monads
1993If a strong monad M is used to define the denotational semantics of a functional language with computations, a product operation x : MX × MY → M ( X × Y) is needed to define the semantics of pairing. Every strong monad is equipped with two standard products, which correspond to left-to-right and right-to-left evaluation.
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Strong regularities in online peer production
Proceedings of the 9th ACM conference on Electronic commerce, 2008Online peer production systems have enabled people to coactively create, share, classify, and rate content on an unprecedented scale. This paper describes strong macroscopic regularities in how people contribute to peer production systems, and shows how these regularities arise from simple dynamical rules. First, it is demonstrated that the probability
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Minimum strong radius of the strong product of paths
Second International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2022), 2023Shuyang Liu, Feng Li
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The g-Extra Connectivity of the Strong Product of Paths and Cycles
Symmetry, 2022Yingzhi Tian, Tian Yingzhi
exaly
On the Laplacians for Strong Product Graphs Based on Polyacene Graphs
Polycyclic Aromatic Compounds, 2022Sakander Hayat +2 more
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