Maximum-index cactus conjecture for signed complete graphs

Let $G_t$ be the cactus graph with $k$ edges and $t$ cycles, with $G_0=K_{1,k}$. Let $\Gamma$ be a signed complete graph of order $n>5$ whose negative edges induce a cactus graph with $k$ edges and $t$ cycles, where $k-t<n$. Cactus maximum-index conjecture. Among all such signed complete graphs, if $\Gamma$ has maximum index, then its negative edges induce the graph $G_t$. This proposed extension of the signed-star extremal problem concerns the structure of the negative-edge subgraph; the supplied source gives no resolution, so the conjecture remains open.