Note: My first question in this site. MSE users asked me to post this question here for better response

I am a Masters student in Pure Mathematics.

I need to do a Masters thesis in "Linear Algebra in Graph Theory" where I will have to publish some original work in our Departmental Journal meant for Masters students.

The Professor supposed to assist me is out of station now for his prior commitments and will be back after 6 months.

I need to publish something significant to graduate. Also I don't have anyone to talk to in our department.

How should I choose some topics and solve some problems in this topic which is worth publication in our journal?

I am feeling helpless.Please suggest me on how to do research in this field.

Please don't close this question as I could not find a better place to ask some help.