You can use the GetNamedItem method to check and see if the attribute is available. If null is returned, then it isn't available. Here is your code with that check in place:
foreach (XmlNode xNode in nodeListName)
{
if(xNode.ParentNode.Attributes.GetNamedItem("split") != null )
{
if(xNode.ParentNode.Attributes["split"].Value != "")
{
parentSplit = xNode.ParentNode.Attributes["split"].Value;
}
}
}