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arXiv · 1604.02908

Degree-associated edge-reconstruction numbers of double-brooms

Meijie Ma·Tingting Zhou
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Abstract

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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Meijie Ma, Tingting Zhou. 2016-04-25. Degree-associated edge-reconstruction numbers of double-brooms. https://arxiv.org/abs/1604.02908

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