%0 Journal Article %T The Roots and Links in a Class of $M$-Matrices %A Xiao-Dong Zhang %J Mathematics %D 2014 %I arXiv %R 10.15352/afa/1396833508 %X In this paper, we discuss exiting roots of sub-kernel transient matrices $P$ associated with a class of $M-$ matrices which are related to generalized ultrametric matrices. Then the results are used to describe completely all links of the class of matrices in terms of structure of the supporting tree. %U http://arxiv.org/abs/1406.7654v1