Research Interests

My field of research is mainly in graph theory, particularly labeling problems (MR05c78) and decomposition of graphs. Trees are also played important role in my research, e.g., graceful, magic and harmonious tree conjectures. I am also interesting problems related with the design, layout, routing etc., of interconnection networks. Click  here  to see the list of publications, abstracts and open problems on  cordial and equitable graph labellings.

I have also interested in the famous four color problem. For my views and ideas for a possible non-computer proof on  this problem click here. For an outline of the three different proofs based on spiral chains:

THE FOUR COLOR THEOREM AND THREE PROOFS

NEW! Illustration of spiral chain “three-plus-one” coloring NEW!

Below I have shown more proper four coloring of USA map with and without neighbor countries (obtained by spiral-chain coloring algorithm). Compare these colorings  with the one shown here.

Still another one which you may compare with the one here.