The Disjoint Paths in Enhanced Hypercube

This paper aims to investigate the internally disjoint paths in Q{n,2}. For this purpose, the structural natures of Q{n, k} (1 ≤ k ≤ n) are investigated in detail. The properties related to the partition of enhanced hypercube Q{n,k}. Based on the results, it has been found that for any two distinct vertices x and y there exists n+1 internally disjoint paths connecting x and y, which traverses all vertices of Q{n,2}. This paper aims to investigate the internally disjoint paths in Q{n,2}. For this purpose, the structural natures of Q{n,k}(1 ≤ k ≤ n) are investigated in detail. The properties related to the partition of enhanced hypercube Q{n,k}. Based on the results, it has been found that for any two distinct vertices x and y there exists n + 1 internally disjoint paths connecting x and y, which traverses all vertices of Q{n,2}.