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Graphs Associated with Algebraic Structure
, M.Sc. Thesis Sharif University of Technology ; Akbari, Saeed (Supervisor)
Abstract
One of the interesting and active area in the last decade is using graph theoretical tools to study the algebraic structures. In this thesis, first we study the intersection graphs of non-trivial submodules of a module, their clique number and their chromatic number. Next, we study the power graph of a group and observe that non-isomorphic finite groups may have isomorphic power graphs, but that finite abelian groups with isomorphic power graphs should be isomorphic. It also is shown that the only finite
group whose automorphism group is the same as that of its power graph is the Klein group of order 4. We study the cozero-divisor graph of R denoted by ′(R) and we show that if ′(R) is a...
group whose automorphism group is the same as that of its power graph is the Klein group of order 4. We study the cozero-divisor graph of R denoted by ′(R) and we show that if ′(R) is a...