Quasi- Laplacian energy of some novel classes of graphs

Abstract

We formulate the relationship of quasi-Laplacian energy of some novel classes of graphs with their corresponding original graphs. The novel graphs in our discussion are the -graph, -graph, -graph, total graph, and their join and corona operations graphs. The whole formulation is based on the relationship between quasi-Laplacian energy and the vertex degrees of the novel graph. It is also noted that quasi-Laplacian energy is closely related with the first Zagreb index, number of vertices and edges of the graph. The exact formulas of quasi-Laplacian energy of novel graphs are obtained in terms of the corresponding quasi-Laplacian energies, the first Zagreb indices, and the number of vertices and edges of the original graphs.