Use this tag for questions in graph theory. Here a graph is a collection of vertices and connecting edges. Use (graphing-functions) instead if your question is about graphing or plotting functions.

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Vertex Reconstruction Conjecture For Asymmetric Graphs

Simple question: (a) Is it known whether all graphs G having trivial aut(G) are vertex reconstructible, and (b) what is the proof if it exists?
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If $G$ is shellable, then $G \backslash \{x_i\}$ is shellable?

A simplicial complex $\Delta$ on the vertex set $\{x_1,\dots,x_n\}$ is shellable if the facets of $\Delta$ can be ordered, say $F_ 1 , . . . , F _s$, such that for all $1 \leq i < j ...