Abstract
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 $\textrm{drn}(G)$, is the minimum number of dacards that suffice to reconstruct $G$. The adversary degree-associated reconstruction number $\textrm{adrn}(G)$ is the least $k$ such that every set of $k$ dacards determines $G$. The analogous parameters for degree-associated edge reconstruction are $\textrm{dern}(G)$ and $\textrm{adern}(G)$. We determine these four parameters for all complete multipartite graphs andtheir complements. The answer is usually $2$ for all four parameters,but there are exceptions in each case.
Citation
Meijie Ma. Huangping Shi. Hannah Spinoza. Douglas West. "DEGREE-ASSOCIATED RECONSTRUCTION PARAMETERS OF COMPLETE MULTIPARTITE GRAPHS AND THEIR COMPLEMENTS." Taiwanese J. Math. 19 (4) 1271 - 1284, 2015. https://doi.org/10.11650/tjm.19.2015.4850
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