Generalized inverses in graph theory

Abstract

Abstract–In this article, some interesting applications of generalized inverses in the graph theory are revisited. Interesting properties of generalized inverses are employed to make the proof of several known results simpler, and several techniques such as bordering method and inverse complemented matrix methods are used to obtain simple expressions for the Moore-Penrose inverse of incidence matrix and Laplacian matrix. Some interesting and simpler expressions are obtained in some special cases such as tree graph, complete graph and complete bipartite graph.

Keywords

• Incidence matrix
• Laplacian matrix
• networks
• resistance distance
• Moore Penrose inverse
• generalized inverse