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On connectivity of the Cartesian product of two graphs
Applied Mathematics and Computation, 1999A graph \(G=(V,E)\) is maximum vertex-connected (maximum edge-connected) if its vertex-connectivity (edge-connectivity) equals \(\Bigl\lfloor \tfrac{2| E| }{| V| }\Bigr\rfloor \). Sufficient conditions for the cartesian product of two graphs to be maximum vertex-connected (maximum edge-connected) are given.
Wen-Sz Chiue, Bih-Sheue Shieh
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On super connectivity of Cartesian product graphs
Networks, 2008AbstractThe super connectivity κ1 of a connected graph G is the minimum number of vertices whose deletion results in a disconnected graph without isolated vertices; this is a more refined index than the connectivity parameter κ. This article provides bounds for the super connectivity κ1 of the Cartesian product of two connected graphs, and thus ...
Min Lü +3 more
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Incidence coloring of Cartesian product graphs
Information Processing Letters, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yue-Li Wang
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The partition dimension of strong product graphs and Cartesian product graphs [PDF]
Discrete Mathematics, 2014 10.1016/j.disc.2014.04.026LetG = (V,E) be a connected graph. The distance between two vertices u, v ? V, denoted by d(u, v), is the length of a shortest u, v-path in G. The distance between a vertex v ? V and a subset P ? V is defined as min{d(v, x) : x ?
Ismael G Yero +2 more
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On the security number of the Cartesian product of graphs
Discrete Applied Mathematics, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Marko Jakovac, Yota Otachi
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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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Factoring cartesian‐product graphs
Journal of Graph Theory, 1994AbstractIn a fundamental paper, G. Sabidussi [“Graph Multiplication,” Mathematische Zeitschrift, Vol. 72 (1960), pp. 446–457] used a tower of equivalence relations on the edge set E(G) of a connected graph G to decompose G into a Cartesian product of prime graphs. Later, a method by R.L. Graham and P.M.
Imrich, Wilfried, Žerovnik, Janez
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DETOUR PEBBLING ON CARTESIAN PRODUCT GRAPHS
South East Asian J. of Mathematics and Mathematical Sciences, 2022Given a distribution of pebbles on the vertices of a connected graph G, a pebbling move is defined as the removal of two pebbles from some vertex and the placement of one of those pebbles on an adjacent vertex. The t - pebbling number of G is the smallest number, ft(G) such that from any distribution of ft(G) pebbles, it is possible to move t pebbles ...
Lourdusamy, A., Nellainayaki, S. Saratha
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Semi-cartesian product of graphs
Journal of Mathematical Chemistry, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Zombie number of the Cartesian product of graphs
Discrete Applied Mathematics, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ali Keramatipour, Behnam Bahrak
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