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%Olesky
%Dale","dolesky@cs.uvic.ca","
\section{Group Inverses of Matrices with Path Graphs} By {\sl M. Catral, D.D. Olesky and P. van den Driessche}.  

\medskip  \noindent A simple formula for the group inverse of a $2 \times 2$ block matrix with a bipartite digraph  is given in terms of the block matrices. This formula is used to give a graph-theoretic  description of the group inverse of an irreducible tridiagonal matrix of odd order with  zero diagonal (which is singular). Relations between the zero/nonzero structures of the  group inverse and the Moore-Penrose inverse of such matrices are given.  An extension of  the graph-theoretic description of the group inverse to singular matrices with tree graphs  is conjectured.
%group inverse, tridiagonal matrix, tree graph, bipartite digraph","15A09","05C50","Minisymposium talk:  MS1  Combinatorial Matrix theory","13:55:37","Mon Mar 24 2008","142.104.68.49"
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