A Topological Approach to the Problem of Ring Structures

Abstract

In complicated molecular structures, these "fundamental rings" can be easily determined, either manually or by means of a programmed computer. The concept of the "ring complex" is defined and suggested as a preliminary screen in literature searches for ring structures. This will save machine time, and so reduce the cost of searches.

Some reflections on the topological structure of covalent molecules

“…The most important of these are illustrated in Figure 7 for some typical organic molecules. Ring structures have been studied by Lederberg (29) and by Fugmann et al (30) with a view to finding new, consistent classifications for such molecules. An algorithm for determining the number of ring atoms in a ring system has been given by Bowman, et al (31).…”

Review of ring perception algorithms for chemical graphs

“…• Its label must be larger than the first vertex in the path (to ensure that each cycle is traced once onlystarting from its lowest vertex label). Nickelsen (1967) graph theory (half-ring tracing) fundamental basis fundamental rings (not the same as a fundamental basis)…”

Mathematical Basis of Ring-Finding Algorithms in CIDS

“…For example, if either the bond 2,7 or 5,7 is selected as bond B and deleted, the algorithm deletes the other (5,7 or 2,7 respectively) and applies Theorem 1 to the remaining structure, a fused pair of 5-atom rings. In the remaining structure the unforked path 9,1,2,3,8 is of length 4 and it is in a 5-atom ring; since for this path P \R\ = 5 5 8 = 2 |P is satisfied, the algorithm records the ring R: (9,1,2,3,8) and deletes the path P, leaving a single 5-atom ring (4,5,6,9,8) which it also records. The reduced structure left after the deletion of the bond B has been found to have an SSSR of two 5-atom rings.…”

“…Therefore the algorithm decides that either of the two 6-atom rings through B, together with the two 5-atom rings (1,2,3,8,9) and (4,5,6,9,8), constitute an SSSR for the original structure.…”

“…If the bond selected for deletion as bond B had been the bond between atoms #8 and #9, the remaining structure would by Theorem 1 have been found to have the SSSR consisting of the 6-atom ring (1,2,7,5,6,91 and the 7-atom ring (1,2,3,8,4,5,6,91. The test that follows would have failed, because the shortest ring through B has only five atoms.…”