If you include node , you cannot include its children (constraint in many problems). So: dp[v][1] = value of + sum of dp[child][0] for all children. If you exclude node , each child can be included or excluded independently: dp[v][0] = sum of max(dp[child][0], dp[child][1]) for all children.
This include/exclude pattern appears in House Robber III, maximum independent set, and similar problems. The insight is that including forces excluding adjacent nodes.