The Induced Subgraph Order on Unlabelled Graphs

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The Induced Subgraph Order on Unlabelled Graphs
A differential poset is a partially ordered set with raising and lowering operators U and D which satisfy the commutation relation DU-UD = rI for some constant r. This notion may be generalized to deal with the case in which there exist sequences of constants {qn}n0 and {rn}n0 such that for any poset element x of rank n, DU(x) = qnUD(x)+rnx. Here, we introduce natural raising and lowering operators such that the set of unlabelled graphs, ordered by G H if and only if G is isomorphic to an induced subgraph of H, is a generalized differential poset with qn = 2 and rn = 2n. This allows one to apply a number of enumerative results regarding walk enumeration to the poset of induced subgraphs.
Craig A. Sloss
Added 11 Dec 2010
Updated 11 Dec 2010
Type Journal
Year 2006
Authors Craig A. Sloss
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