The Laplacian and distance matrix of a signed tree

Let N and \widetilde{D} be net Laplacian and net distance matrices of a signed tree, respectively. The inverse (resp. group inverse) of \widetilde{D} is obtained if it is nonsingular (resp. singular), which extend the inverse formula obtained by Graham and Lov\'{a}sz for distance matrix of a unsigned tree. The interlacing inequality connecting the eigenvalues of \widetilde{D} and N of a signed tree is also obtained.

کلیدواژه ها:

signed tree ، net distance matrix ، net Laplacian matrix ، group inverse