THE SUPER SPANNING CONNECTIVITY AND SUPER SPANNING LACEABILITY OF TORI WITH FAULTY ELEMENTS
Jing Li, Di Liu, Jun Jie Yuan · International Journal of Foundations of Computer Science · 2013
A k-container of a graph G is a set of k internally disjoint paths between two distinct vertices. A k-container of G is a k*-container if it contains all vertices of G. A graph G is k*-connected if there exists a k*-container between any two distinct vertices, and a bipartite graph G is k*-laceable if there exists a k*-container between any two vertices from different partite sets of G. A k-connected graph (respectively, bipartite graph) G is super spanning connected (respectively, laceable) if G is r*-connected (r*-laceable) for any r with 1 ≤ r ≤ k. This paper shows that the two-dimensional torus Torus (m, n), m, n ≥ 3, is super spanning connected if at least one of m and n is odd and super spanning laceable if both m and n are even. Furthermore, the super spanning connectivity and spanning laceability of tori with faulty elements have been discussed.