Embedding meshes into locally twisted cubes

Embedding Complete Binary Trees into Locally Twisted Cubes

“…We prefix the label of each node of CBT 4 in the Figure 2 (a) with 0, and prefix the label of each node of CBT 4 in the Figure 2 (b) with 1, and then, we link the roots of this two complete binary trees with two edges (00010,01000) and (00010,11010). It upper steps can construct CBT 5 . Edge (00010,01000) of CBT 5 is mapping to the path P 1 : 00010− > 01010− > 01000 of LT Q 5 and edge (00010,11010) of CBT 5 is mapping to the path P 2 : 00010− > 10010− > 11010 of LT Q 5 , see Figure 3.…”

“…Furthermore, LT Q n was proved to be (n − 2)-pancyclic [2], for any integer n ≥ 3. And some other properties of locally twisted cubes were discussed [8], [7], [5].…”

Embedding meshes into twisted-cubes

“…Graph embedding has significant applications in transplanting parallel algorithms developed for one network to a different one, and allocating concurrent processes to processors in the network. As the popular interconnection networks used in parallel computing, meshes [8,10,16,17,23,28], paths (or linear arrays) [7,[12][13][14][15]22,25,26,32], cycles [2][3][4]6,18,19,29,30], and trees [5,9,33] are the fundamental guest graphs.…”

“…Therefore, embedding of meshes is a very important issue in interconnection networks. In particular, many results on embedding of meshes into variations of hypercubes have been obtained in recent years [8,10,16,17,23].…”

“…That is, for any integer n P 1, a 2  2 nÀ1 mesh can be embedded into both TN n and LTQ n with dilation 1 and expansion 1 [16]. On the other hand, a 2  2 nÀ1 mesh can be embedded into LTQ n with dilation 1 [16], while the result (2) shows that an m  k mesh cannot be embedded into TN n with dilation 1 for any integers m and k with m P 3 and k P 3. Therefore, we have to consider embedding of the m  k mesh with dilation 2 when m P 3 and k P 3 in LTQ n and thus we prove the result (3) in this paper.…”