One-to-Many Node Disjoint Path Covers on WK-Recursive Networks

Many-to-Many Disjoint Path Covers in Double Loop Networks

Paired Many-to-Many Disjoint Path Covers in Recursive Circulants and Tori

A paired many-to-many -disjoint path cover (paired -DPC) of a graph  is a set of  disjoint paths joining  distinct source-sink pairs in which each vertex of  is covered by a path. In this paper, we investigate disjoint path covers in recursive circulants   with ≥  and tori, and show that provided the number of faulty elements (vertices and/or edges) is  or less, every nonbiparti...

Paired many-to-many disjoint path covers in faulty hypercubes

A paired many-to-many k-disjoint path cover (k-DPC for short) of a graph is a set of k disjoint paths joining k distinct source-sink pairs that cover all the vertices of the graph. Extending the notion of DPC, we define a paired many-to-many bipartite k-DPC of a bipartite graph G to be a set of k disjoint paths joining k distinct source-sink pairs that altogether cover the same number of vertic...

One-to-one disjoint path covers on multi-dimensional tori

One-to-one disjoint path covers on multi-dimensional tori Jing Li, Di Liu, Yuxing Yang & Jun Yuan a School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024, China b School of Mathematical Sciences, Shanxi University, Taiyuan 030006, China c College of Mathematics and Information Science, Henan Normal University, XinXiang 453007, China Accepted author version post...

Paired many-to-many disjoint path covers of hypertori

Let n be a positive integer, and let d = (d1, d2, . . . , dn) be an n-tuple of integers such that di ≥ 2 for all i. A hypertorus Q d n is a simple graph defined on the vertex set {(v1, v2, . . . , vn) : 0 ≤ vi ≤ di − 1 for all i}, and has edges between u = (u1, u2, . . . , un) and v = (v1, v2, . . . , vn) if and only if there exists a unique i such that |ui − vi| = 1 or di − 1, and for all j ≠ ...