I am working on a graph theory paper with two of my friends. The problem stated in the paper is solved by me. However, our supervisor professor pointed out that in all of the graph theory journals (and other mathematics journals as well), names of authors are sorted by an alphabetic order which puts me in the third position after one of my friends who was mainly in charge of half of the editings (which I greatly thank his efforts) and our supervisor professor.
I wonder if there is any way to point out who was the main contributor in a graph paper or not.
I think this may be a very deciding factor in being accepted by a good university for a master program because we can only have a few papers before graduation.
I wanted to see if there is any way to point out who was the main contributor in a graph paper or not?
Generally not. In pure mathematics it's extremely unconventional to use any author ordering other than alphabetical. You could try, but it will look weird and attract negative attention, and nobody will be quite sure how to interpret it. In particular, you run the risk of having people think "this jerk insisted on being listed first despite the near-universal use of alphabetical order". I virtually never see papers with any other author ordering, and I would not recommend it.
It's also rare and considered awkward to include any discussion in the paper of who contributed what. One reason is that it's difficult to write such a discussion fairly. For example, suppose your collaborators try three approaches that fail before you find one that works. Reasonable people could disagree as to whether your collaborators were obviously on the wrong track all along, or whether they pointed the way to the solution by eliminating other plausible methods. (The general principle is that if your collaborators aren't useful, then you shouldn't be working with them. Turning this around, if they are useful enough that you are happy to work with them before the problem is solved, then you can't retroactively decide that they weren't useful enough afterwards.)
The flip side of this is that the standards for being an author are fairly demanding, and coauthors should have seriously worked on the mathematics itself. In particular, supervising the project or editing the paper are not by themselves sufficient for coauthorship. But it's reasonable for these people to be coauthors if they worked on the problem with you, even if you were the one who ended up making the decisive contribution.
I think it may be a very deciding factor in being accepted by a good university for a master program because we can only have a few papers before graduation.
The usual way this information is conveyed is a letter of recommendation from your supervisor, who can highlight the role you played in the project.