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Mutual-Visibility Sets in Cartesian Products of Paths and Cycles [PDF]
Results in MathematicsFor a given graph G, the mutual-visibility problem asks for the largest set of vertices M ⊆ V (G) with the property that for any pair of vertices u, v ∈ M there exists a shortest u, v-path of G that does not pass through any other vertex in M. The mutual-
Aleksander Vesel
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Counting stable sets on Cartesian products of graphs [PDF]
Discrete Mathematics, 1998 We study the generating functions for the number of stable sets of all cardinalities, in the case of graphs which are Cartesian products by paths, cycles, or trees. Explicit results are given for products by cliques.
Florence Forbes, Bernard Ycart
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Using Cartesian Product for Animation
The Journal of Visualization and Computer Animation, 2000AbstractIn the field of geometric modelling for animation, 4D modelling (time being the fourth dimension) seems to be a natural extension of 3D modelling. But time dimension is not easy to apprehend and 4D objects are difficult to interpret and to control in general.
Xavier Skapin, Pascal Lienhardt
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On the crossing numbers of Cartesian products with paths [PDF]
Journal of Combinatorial Theory Series B, 2007 Using a newly introduced operation on graphs and its counterpart on graph drawings, we prove the conjecture of Jendrol' and Ščerbová from 1982 about the crossing number of the Cartesian product K1,m□Pn.
Bokal, Drago
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American Journal of Mathematics, 1969
0. Introduction. Let as be an arc in the interior In of the n-cell In and let X be the quotient space I"/ac obtained by shrinking a to a point. According to Kwun and Raymond [4], X X 12 is an (n + 2)-cell. The crucial tool in their proof is the result of Andrews-Curtis that, under the above conditions, In/a X R1 is homeomorphic to In XR1.
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0. Introduction. Let as be an arc in the interior In of the n-cell In and let X be the quotient space I"/ac obtained by shrinking a to a point. According to Kwun and Raymond [4], X X 12 is an (n + 2)-cell. The crucial tool in their proof is the result of Andrews-Curtis that, under the above conditions, In/a X R1 is homeomorphic to In XR1.
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On the Discrepancy for Cartesian Products
Journal of the London Mathematical Society, 2000We prove that the discrepancy for the family of Cartesian products \(B_1\times B_2\subseteq \mathbb{R}^4\), where \(B_1\) and \(B_2\) are circular discs in the plane, is \(O(n^{1/4+\varepsilon})\) for an arbitrarily small constant \(\varepsilon>0\), i.e. essentially the same as that for discs in the plane.
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Connectivity of Cartesian Product of Hypergraphs
Bulletin of the Iranian Mathematical Society, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Na, Meng, Jixiang, Tian, Yingzhi
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Homogeneous Cartesian products [PDF]
Australas. J Comb., 2002 Summary: A graph \(G\) is 1-homogeneous if certain isomorphisms between similarly embedded induced subgraphs of \(G\) extend to automorphisms of \(G\). We show that the only connected composite 1-homogeneous graphs are the cube, and \(K_n\times K_2\) and \(K_n\times K_n\) with \(n\geq 2\).
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Panconnectivity of Cartesian product graphs
The Journal of Supercomputing, 2009A graph G of order n (?2) is said to be panconnected if for each pair (x,y) of vertices of G there exists an xy-path of length ? for each ? such that d G (x,y)???n?1, where d G (x,y) denotes the length of a shortest xy-path in G. In this paper, we consider the panconnectivity of Cartesian product graphs.
You Lu 0002, Jun-Ming Xu 0001
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