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$G$-reconstruction of graphs

Bhalchandra D. Thatte
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Abstract

Let $G$ be a group of permutations acting on an $n$-vertex set $V$, and $X$ and $Y$ be two simple graphs on $V$. We say that $X$ and $Y$ are $G$-isomorphic if $Y$ belongs to the orbit of $X$ under the action of $G$. One can naturally generalize the reconstruction problems so that when $G$ is $S_n$, the symmetric group, we have the usual reconstruction problems. In this paper, we study $G$-edge reconstructibility of graphs. We prove some old and new results on edge reconstruction and reconstruction from end vertex deleted subgraphs.

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Bhalchandra D. Thatte. 2006-08-03. $G$-reconstruction of graphs. https://arxiv.org/abs/math/0608071

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