  The adjoint polynomial of $G$ is \[h(G,x)=\sum_{k=1}^n(-1)^{n-k}a_k(G)x^k,\]
where $a_k(G)$ denotes the number of ways one can cover all vertices of the
graph $G$ by exactly $k$ disjoint cliques of $G$. In this paper we show the the
adjoint polynomial of a graph $G$ is a simple transformation of the
independence polynomial of another graph $\widehat{G}$. This enables us to use
the rich theory of independence polynomials to study the adjoint polynomials.
In particular we a give new proofs of several theorems of R. Liu and P.
Csikv\'{a}ri.
