Jennifer,
Thank you for the quick response. Unfortunately maybe my question was a little off.
First, I misstated how EditVertices was instigated, its done using the graphic, not the graphic.Geometry. Thanks for ointing that out.
Also, in both your response and the sample, which I was familiar with, the code refers to getting the edits from a feature layer, which of course has the SaveEdits method. I'm trying to do essentially the same thing with a graphics layer that is NOT a feature layer. The layer type I'm actually wanting to edit is based on the KmlLayer examples found elsewhere in these forums and is not based on FeatureLayer.
Maybe that is the problem, I should be using a feature layer even though I do not get them directly from ArcServer? Or how to get the .SaveEdits functionality from a GraphicsLayer without the cast to FeatureLayer.