The degree-associated edge-reconstruction conjecture for disconnected equal-component graphs

Let $G$ be as in Theorem 4.2: a disconnected graph whose non-trivial components are all isomorphic to a graph $H$. Let $dern(G)$ denote the minimum number of degree-associated edge-cards needed to determine $G$ up to isomorphism. Equal-component degree-associated edge-reconstruction conjecture. If the hypothesis $\delta(H)\geq 3$ in Theorem 4.2 is replaced by the exclusions

$$H\neq K_{1,3},\qquad H\neq K_{1,2},\qquad H\neq K_{2,3},$$

then $dern(G)\leq 2$.

The conjecture is motivated by the observation that the three excluded component types give the exceptional examples known in the discussion, while the stated bound is proved under the stronger minimum-degree condition. Its general status is left open in the supplied text.