On the Moore-Penrose pseudo-inversion of block symmetric matrices and its application in the graph theory

The purpose of this paper is to analyze the Moore-Penrose pseudo-inversion symmetric real matrices with application in graph theory. We introduce a novel concept positively and negatively pseudo-inverse graphs. also give sufficient conditions on elements block matrix yielding an explicit form its pseudo-inversion. Using we can construct graphs for class which are constructed from original by adding pendent vertices or pendant paths.