# Definition for an outer cycle in formal English

When defining a thing based on the mathematical perspective, I am using the following construction:

This cycle can be defined as Outer Cycle: The closed path between two vertices whose starting and ending vertices are the same and (the path) running along the vertices where they are located most outer edges of the original graph.

How could this be modified avoiding unnecessary things while making clear idear to reader.

For example, my outer cycle looks like red cycle in figure below.

• Your question about whose is addressed in this question. However, this sentence has other problems; may I suggest that you rewrite along the lines of your very well-constructed earlier question, with the distinct propositions set out in detail, so we may address those other problems? Otherwise the question is likely to be closed as a duplicate. – StoneyB on hiatus Mar 23 '13 at 13:48
• @StoneyB: yes, as you pointed out, this post and earlier question give same meaning. but honestly, i am addressing two different cases. here, it is the mathematical definition and other one is for the result what i got. anyway, i will try to update the post as my best – niro Mar 23 '13 at 13:57

1. Whose is perfectly acceptable here; but placing whose after two vertices implies that what follows (starting and ending vertices are the same) is attributed to the two vertices. I think what you mean is that the starting and ending vertices of the path are the same.

2. Vertex here seems to denote two different things: a) a point on a graph, and b) the same point considered as a component of a path.

3. The participle running is so distant from its subject path that the connection is lost. Furthermore, when you are including two components in a definition like this it is best to employ the same syntactical construction for both.

4. In English we say outermost rather than most outer.

These problems might be addressed by something like this:

This Outer Cycle is the closed path which starts and ends on the same vertex and runs through all the outermost vertices of the original graph.

OR

This Outer Cycle is the closed path which starts and ends on the same vertex and runs along the outermost edge of the original graph.