  A {\em word labeled oriented graph} (WLOG) is an oriented graph $\cal G$ on
vertices $X=\{ x_1,\ldots ,x_k\}$, where each oriented edge is labeled by a
word in $X^{\pm1}$. WLOGs give rise to presentations which generalize Wirtinger
presentations of knots. WLOG presentations, where the underlying graph is a
tree are of central importance in view of Whitehead's Asphericity Conjecture.
We present a class of aspherical world labeled oriented graphs. This class can
be used to produce highly non-injective aspherical labeled oriented trees and
also aspherical cyclically presented groups.
