Combinatorics Question

Given a complete graph with nodes N:

Whats the most uniform way to traverse it for any non-triangular number N?

This has driven me insane for a couple of years now, is there even a solution?

>>3
It makes even less sense: there's no need to provide any traversal algorithm like you did, because all nodes in a complete graph are indistinguishable and therefore all traversals are isomorphic. In a sense there exists one traversal, if you ignore arbitrary way you might number the nodes.