Homotopy classification of homogeneous projections in the corona algebra of C(X,B) for a graph X

In this paper we consider certain projections in the corona algebra of C ( X ) ⊗ B for X a directed graph and B a stable C ⁎ -algebra of which the multiplier algebra has real rank zero. Assuming a kind of homogeneity on the projections we characterize when two such projections are homotopy equivalent. As a result, for a simple graph we show that such projections are always homotopic.