An observation on the bisectional interconnection networks

It is shown that the bisectional interconnection network (BIN) of 2ⁿ nodes for any even n is isomorphic to the n -dimensional folded hypercube (FHC), an n-dimensional hypercube with additional edges between any two nodes that are of Hamming distance n apart. This observation leads to simplification for the proofs of many interesting properties for the BIN. Inspired by the isomorphism between BIN and FHC, the class of topologies in which nodes are represented by bit strings and two nodes are adjacent if and only if the bitwise Exclusive-OR of their addresses fall in a set of predefined bit string patterns are studied. A few theorems are given to characterize the topology from the mathematical properties of the binary matrix derived from the definition of edges