Caporossi–Cvetković–Gutman–Hansen conjecture on maximal energy of unicyclic graphs

Let $C_n$ be the cycle on $n$ vertices. Let $P_n^6$ be the unicyclic graph obtained by connecting a vertex of the cycle $C_6$ to a leaf of the path $P_{n-6}$. For a graph $G$ with adjacency-matrix eigenvalues $\lambda_1,\ldots,\lambda_n$, its energy is

$$E(G)=\sum_{i=1}^n|\lambda_i|.$$

Caporossi–Cvetković–Gutman–Hansen conjecture. Among all unicyclic graphs on $n$ vertices, the cycle $C_n$ has maximal energy if $n\leq 7$ or $n\in\{9,10,11,13,15\}$. For all other values of $n$, the unicyclic graph with maximal energy is $P_n^6$.

The conjecture identifies the extremal unicyclic graph by the number of vertices and concerns the adjacency-spectrum energy of graphs. The supplied text does not state whether the conjecture has been resolved.