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

• Type: Journal
• Year: 2002
• Where: SIAMDM
• Authors: Edgar M. Palmer, Ronald C. Read, Robert W. Robinson
• Keywords: Claw-free Cubic Graphs, Cubic Graph, Exponential Generating Function, SIAMDM 2002