The two-equal-disjoint path cover problem of the hierarchical crossed cube ∗

To construct parallel paths among nodes in interconnection networks is an important issue concerned with efficient data transmission. Embedding of paths have attracted much attention in the parallel processing. A graph G is globally twoequal-disjoint path coverable (GTEDPC) if for any two distinct pairs of vertices a, b and c, d of G, there exist two disjoint paths P and Q satisfy that (1) P (Q, respectively) joins a and b (c and d, respectively), (2) |P | = |Q|, and (3) V (P ∪ Q) = V (G). The hierarchical crossed cube is a new hierarchical interconnection network. In this paper, we study the globally two-equal-disjoint path cover property of HCC(k, n) for k ≥ 1 and n ≥ 5.