$phi^4$-Theory: Sub-Diagram zero $Rightarrow$ Diagram zero?

Considering a bosonic $phi^4$-theory:

If I know that a certain connected Feynman diagram has a vanishing contribution. Does this imply that all larger connected diagrams containing this diagram are also vanishing in the general case?

In my specific problem, all diagrams contributing to the self-energy are zero. Is the implication true for this case?

A simple example would be: If the order one tadpole diagram and larger diagrams containing this tadpole diagram.