The Path-Pairability Number of Product of Stars

Abstract

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
• 05c38
• 05c40