Specify an upper bound of the size m of R with the big O notation
Are upper bound of the size m and runtime two different concept?


The concept is just upper bounding. It doesn't matter whether you're bounding the number of vertices in a graph, the number of steps a program takes to execute, or the number of elephants in India&nbsp;&ndash; it's just an upper bound.

Probably the first time most CS students see big-O notation is in the context of runtimes and it's a common mistake to assume that big-O somehow means runtime. But it doesn't. This is the same mistake as, "The first time I saw numbers, they referred to somebody's height. Therefore, numbers mean height."