Connectivity and Matching Preclusion for Leaf-Sort Graphs.

A multiprocessor system and interconnection network have a underlying topology, which is usually presented by a graph, where nodes represent processors and links represent communication links between processors. The (conditional) matching preclusion number of a graph is the minimum number of edges whose deletion leaves the resulting graph (with no isolated vertices) that has neither perfect matchings nor almost perfect matchings. In this paper, we prove that (1) the connectivity (edge connectivity) of the leaf-sort graph CFn is 3n-3/2 (3n-3/2) for odd n and 3n-4/2 (3n-4/2) for even n; (2) CFn is super edge-connected; (3) the matching preclusion number of CFn is 3n-3/2 for odd n and 3n-4/2 for even n; (4) the conditional matching preclusion number of CFn is 3n - 5 for odd n and n >= 3, and 3n - 6 for even n and n >= 4.