Counting Claw-Free Cubic Graphs

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Counting Claw-Free Cubic Graphs
Let Hn be the number of claw-free cubic graphs on 2n labeled nodes. Combinatorial reductions are used to derive a second order, linear homogeneous differential equation with polynomial coefficients whose power series solution is the exponential generating function for {Hn}. This leads to a recurrence relation for Hn which shows {Hn} to be P-recursive and which enables the sequence to be computed efficiently. Thus the enumeration of labeled claw-free cubic graphs can be added to the handful of known counting problems for regular graphs with restrictions which have been proved P-recursive. Key words. labeled graph counting, claw-free graph, cubic graph, exponential generating function, P-recursive sequence AMS subject classifications. 05A15, 05C30 PII. S0895480194274777
Edgar M. Palmer, Ronald C. Read, Robert W. Robinso
Added 23 Dec 2010
Updated 23 Dec 2010
Type Journal
Year 2002
Authors Edgar M. Palmer, Ronald C. Read, Robert W. Robinson
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