Computing the Energy of Certain Graphs Based on Vertex Status

Background The concept of Huckel molecular orbital theory is used to compute the graph energy numerically and graphically on the base of the status of a vertex.Objective Our aim is to explore the graph energy of various graph families on the base of the status adjacency matrix and its Laplacian version.Methods We opt for the technique of finding eigenvalues of adjacency and Laplacian matrices constructed on the base of the status of vertices.Results We explore the exact status sum and Laplacian status sum energies of a complete graph, complete bipartite graph, star graphs, bistar graphs, barbell graphs and graphs of two thorny rings. We also compared the obtained results of energy numerically and graphically.Conclusion In this article, we extended the study of graph spectrum and energy by introducing the new concept of the status sum adjacency matrix and the Laplacian status sum adjacency matrix of a graph. We investigated and visualized these newly defined spectrums and energies of well-known graphs, such as complete graphs, complete bi-graphs, star graphs, friendship graphs, bistar graphs, barbell graphs, and thorny graphs with and cycles.