Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Degree-associated edge-reconstruction numbers of double-brooms   An edge-deleted subgraph of a graph $G$ is an {\it edge-card}. A {\it decard}
consists of an edge-card and the degree of the missing edge. The {\it
degree-associated edge-reconstruction number} of a graph $G$, denoted
$\dern(G)$, is the minimum number of decards that suffice to reconstruct $G$.
The {\it adversary degree-associated edge-reconstruction number} $\adern(G)$ is
the least $k$ such that every set of $k$ decards determines $G$. We determine
these two parameters for all double-brooms. The answer is usually $1$ for
$\dern(G)$, and $2$ for $\adern(G)$ when $G$ is double-broom. But there are
exceptions in each case.

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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci