We propose a new puzzle: Label the eight vertices of cube using distinct integers between 0 and 12 (both inclusive) such that induced labeling each edge, given by sum labels its end points, causes edges to be labeled with odd numbers 1, 3, … 23. Any solution puzzle is called super odd-sum labeling. deftly discover all cube.

We prove the following results : (a) The Cube-Connected Cycles network of dimension n is a subgraph of the Butterry network of dimension n. (b) The Shuue-Exchange network of dimension n is a subgraph of the DeBruijn network of dimension n.

In this paper, we investigate extremal volumes of non-central slices of the unit cube. The case of central hyperplane sections is known and was studied in [Ha], [Ba1] [He1]. The case of non-central sections, i.e. when we dictate that the hyperplane must be a certain distance t > 0 from the center of the cube, is open in general and the same is true about sections of the unit cube by slabs, with...

The Möbius cube MQn and the crossed cube CQn are two important variants of the hypercube Qn. This paper shows that for any two different vertices u and v in G ∈ {MQn,CQn} with n 3, there exists a uv-path of every length from dG(u, v)+ 2 to 2n − 1 except for a shortest uv-path, where dG(u, v) is the distance between u and v in G. This result improves some known results.  2005 Elsevier B.V. All ...