  Let G be a simple connected graph with n vertices, and let d_i be the degree
of the vertex v_i in G. The extended adjacency matrix of G is defined so that
the ij-entry is 1/2(d_i/d_j+d_j/d_i) if the vertices v_i and v_j are adjacent
in G, and 0 otherwise. This matrix was originally introduced for developing
novel topological indices used in the QSPR/QSAR studies. In this paper, we
consider extremal problems of the largest eigenvalue of the extended adjacency
matrix (also known as the extended spectral radius) of trees. We show that
among all trees of order n>= 5, the path Pn(resp., the star Sn) uniquely
minimizes (resp., maximizes) the extended spectral radius. We also determine
the first five trees with the maximal extended spectral radius.
