On the Vector Degree Matrix of a Connected Graph - Nasr A. Zeyada; Anwar Saleh; Majed Albaity; Amr K. Amin (Journal of Mathematics)
A matrix representation of the graph is one of the tools to study the algebraic structure and properties of a graph. In this paper, by defining the vector degree matrix of graph G, we provide a new matrix representation of the graph. For some standard graphs, VD-eigenvalues, VD-spectrum, and VD-energy values are defined and calculated. Moreover, we calculate the VD-matrix and calculate the VD-eigenvalues for graphs representing the chemical composition of paracetamol and tramadol.