A vertex-deleted subgraph of a graph G is a card. A dacard specifies the degree of the deleted vertex along with the card. The adversary degree-associated reconstruction number adrn(G) is the least k such that every set of k dacards determines G. We determine adrn(D m,n,p ), where the double-broom D m,n,p with p ≥ 2 is the tree with m + n + p vertices obtained from a path with p vertices by appending m leaves at one end and n leaves at the other end. We determine adrn(D m,n,p ) for all m, n, p. For 2 ≤ m ≤ n, usually adrn(D m,n,p ) = m + 2, except adrn(D m,m+1,p ) = m + 1 and adrn (D m,m+2,p There are exceptions when (m, n) = (2, 3) or p = 4. For m = 1 the usual value is 4, with exceptions when p ∈ {2, 3} or n = 2.
A vertex-deleted subgraph of a graph G is a card. A dacard consists of a card and the degree of the missing vertex. The degree-associated reconstruction number of a graph G, denoted drn(G), is the minimum number of dacards that suffice to reconstruct G. The adversary degree-associated reconstruction number adrn(G) is the least k such that every set of k dacards determines G. The analogous parameters for degree-associated edge reconstruction are dern(G) and adern(G). We determine these four parameters for all complete multipartite graphs and their complements. The answer is usually 2 for all four parameters, but there are exceptions in each case.
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