Cycle and Path Embedding on 5-ary N-cubes

Cycle and Path Embedding on 5-ary N-cubes

We study two topological properties of the 5-ary n-cube Qn. Given two arbitrary distinct nodes x and y in Q 5 n, we prove that there exists an x-y path of every length ranging from 2n to 5n−1, where n ≥ 2. Based on this result, we prove that Qn is 5-edge-pancyclic by showing that every edge in Qn lies on a cycle of every length ranging from 5 to 5. Mathematics Subject Classification. 68R10, 68R...

On $n$-ary Hypergroups and Fuzzy $n$-ary Homomorphism

ON BOTTLENECK PARTITIONING k-ARY n-CUBES

/raph partitioning is a topic of extensive interest, with applications to parallel processing. In this context graph nodes typically represent computation, and edges represent communication. One seeks to distribute the workload by partitioning the graph so that every processor has approximately the same workload, and the communication cost (measured as a fimction of edges exposed by the partiti...

Augmented k-ary n-cubes

We define an interconnection network AQn,k which we call the augmented kary n-cube by extending a k-ary n-cube in a manner analogous to the existing extension of an n-dimensional hypercube to an n-dimensional augmented cube. We prove that the augmented k-ary n-cube AQn,k has a number of attractive properties (in the context of parallel computing). For example, we show that the augmented k-ary n...

Path bundles on n-cubes

A path bundle is a set of 2a paths in an n-cube, denoted Qn, such that every path has the same length, the paths partition the vertices of Qn, the endpoints of the paths induce two subcubes of Qn, and the endpoints of each path are complements. This paper shows that a path bundle exists if and only if n > 0 is odd and 0 ≤ a ≤ n − ⌈log 2 (n + 1)⌉.