For a $\mathbb{Z}_p$-covering of connected graphs, an analogue of Iwasawa's class number formula describes the growth of the number of spanning trees in terms of Iwasawa $λ$- and $μ$-invariants. In this paper, we show that any pair $(λ, μ)$ can be realized as the Iwasawa invariants of an unramified $\mathbb{Z}_p$-covering of a bouquet, provided that the necessary condition that $λ$ is odd is satisfied. We further show that any pair $(λ, μ)$, without a parity condition, can be realized if we allow ramified $\mathbb{Z}_p$-coverings.