What is the point of a less or canceled equal operator? In my computing science script there is a really weird symbol:

What does this symbol mean? Is it any different from '<'? Is this just to higlight the fact that it is not equal? I'm confused ...
Edit: I should mention that R(N,m_0) is a graph (V,E) and m1,m2 element of V.

In this symbol list, it is called "LESS-THAN AND SINGLE-LINE NOT EQUAL TO", $\lneq$. There is also "GREATER-THAN AND SINGLE-LINE NOT EQUAL TO", $\gneq$. These are apparently variants on $\lneqq$ and $\gneqq$, so your interpretation of smaller than but not equal to is likely correct.
