Graphs without vertices of degree n-1 are uniquely determined by their Bell colouring graphs, which encode partitions into independent sets.
Then in both cases, there are exactly five partitions ofG′ i into at leastk i parts, and with one exception these partitions are all adjacent to each other inB≥k1(Gi)
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Reconstructing a graph from its Bell colouring graph
Graphs without vertices of degree n-1 are uniquely determined by their Bell colouring graphs, which encode partitions into independent sets.