On the Net Distance Matrix of a Signed Block Graph

Abstract

A connected signed graph Ġ, where all blocks of it are positive cliques or negative cliques (of possibly varying sizes), is called a signed block graph. Let A, N and D̃ be adjacency, net Laplacian and net distance matrices of a signed block graph, respectively. In this paper the formulas for the determinant of A and D̃ were given firstly. Then the inverse (resp. Moore-Penrose inverse) of D̃ is obtained if it is nonsingular (resp. singular), which is the sum of a Laplacian-like matrix and at most two matrices with rank 1.