Geodesic
The Path-Pairability Number of Product of Stars
Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 4, pp. 909-924

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The study of a graph theory model of certain telecommunications network problems lead to the concept of path-pairability, a variation of weak linkedness of graphs. A graph G is k-path-pairable if for any set of 2k distinct vertices, si, ti, 1 ≤ i ≤ k, there exist pairwise edge-disjoint si, ti-paths in G, for 1 ≤ i ≤ k. The path-pairability number is the largest k such that G is k-path-pairable. Cliques, stars, the Cartesian product of two cliques (of order at least three) are ‘fully pairable’; that is ⌊n/2⌋-pairable, where n is the order of the graph. Here we determine the path-pairability number of the Cartesian product of two stars.
Keywords: path-pairability, weak linkage, Cartesian product, star-like network, telecommunications network 
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Jobson, Adam S.; Kézdy, André.; Lehel, Jenő; Mészáros, Gábor. The Path-Pairability Number of Product of Stars. Discussiones Mathematicae. Graph Theory, Tome 39 (2019) no. 4, pp. 909-924. http://geodesic.mathdoc.fr/item/DMGT_2019_39_4_a11/