Graphs associated with Rings, Groups, and Vector Spaces

I suggest that you visit the wb page of one of the leading figures in Graph Theory: Douglas B. west, you will find a lot of materials, open problems and so on.

https://faculty.math.illinois.edu/~west/

Graph theoritical way for Segmentation of images for efficient identification of suspicious parts

Ramanujan Graph may be an interesting area in graph theory.

Domination Theory is another one.

Spectral graph theory is one of the emerging areas in graph theory, which has several applications. For details, you can go through the book on "Graphs and Matrices" by R.B. Bapat.

Mathematical Combinatorics, or mathematcics over graphs and complex network, etc. is the central source for creation by graphs,. More new notions can be found in the www.mathcombin.com/notions.

1.Domination Theory in Graphs

2.Colouring/Labeling/Facterization of Graphs

3.Spectral Graph Theory

Graphs associated with Rings, Groups, and Vector Spaces

Graph theory interlink with Harmonic Analysis is also an interesting topic Like the paper Article Best constants for the Hardy-Littlewood maximal operator on ...

also the paper Article Geometric properties of infinite graphs and the Hardy-Little...

Hope so these will be interesting for you.

This is my research paper

https://dergipark.org.tr/hujms/issue/42398/471101

Topological indices in medical field.

Graphs colouring , Domination Theory in Graphs ، Colouring/Labeling/Facterization of Graphs , Spectral Graph Theory

Factorization is one of the interesting topics in graph theory, which has many applications for research.