Pseudo-Von Neumann Regular Graph of Commutative Rings

This book introduces a new definition of Von Neumann regular graph of commutative ring R called Pseudo-Von Neumann regular graph of commutative ring. It is denoted by P-VG(R), where the vertices of the graph represent the elements of R, such that there is an edge between the two vertices a and b if and only if a=a^2 b or b=b^2 a. This study reaches important results related to P-VG(R) like chromatic number of some P-VG(R) graphs and chromatic numbers of P-VG(R) graphs of Cartesian product of rings, as well as computed topological indices such as eccentricity, connectivity, sum connectivity, forgotten, first and second zegrab, Atom Bond Connectivity, Geometric-Arithmetic, and Harmonic indices of Pseudo-Von Neumann regular graphs of R=Z_p and R=Z_(p^i ).