  A shelling of a graph, viewed as an abstract simplicial complex that is pure
of dimension 1, is an ordering of its edges such that every edge is adjacent to
some other edges appeared previously. In this paper, we focus on complete
bipartite graphs and trees. For complete bipartite graphs, we obtain an exact
formula for their shelling numbers. And for trees, we relate their shelling
numbers to linear extensions of tree posets and bound shelling numbers using
vertex degrees and diameter.
