@SamHopkins; Yes true but is this not a part of Algebraic Graph theory?

I am really grateful for this answer, i was looking for answers like these from the morning. The more I asked about it here, the more I got discouraged

okay but my question is did people start associating graphs to algebraic structures just because it gave good results, the fact which you mentioned about cayley graphs have been used very recently for solving a very specific problem although cayley graphs existed from 1800 A.D

Would you mind elaborating a bit?

Yes I checked it, it says if every finitely generated group having order of each element finite is finite or not but how do you bring Cayley Graphs into picture

I am looking forward to some answers from you

Can you please explain how a Cayley Graph can be used to solve any problems in Algebra, Suppose I have a problem X in Group Theory, How can I solve X by associating Cayley Graph to the given group

Your answer really goes into what I have been looking for since the morning

So, does it mean that the primary reason we associate a graph to an algebraic structure is we want to visualise and help our brains?

I understand the last paragraph where you write "Suppose.." , But I am looking for some concrete examples, will you be able to show me some examples where I can find a property of ring from its graph structire

@spin; thank you very much for highlighting the main motivation of my question, i was looking for exactly the answer of this question

Did you just copy paste the abstract? Its okay, i am thankful for all the effort you are putting in but its not helping,