NDLI: Counting Claw-Free Cubic Graphs

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Palmer, Edgar M. Read, Ronald C. Robinson, Robert W.
Copyright Year	2002
Abstract	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.
Starting Page	65
Ending Page	73
Page Count	9
File Format	PDF
ISSN	08954801
DOI	10.1137/S0895480194274777
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	1
Volume Number	16
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-08-01
Access Restriction	Subscribed
Subject Keyword	exponential generating function Enumeration in graph theory claw-free graph Exact enumeration problems, generating functions labeled graph counting cubic graph P-recursive sequence
Content Type	Text
Resource Type	Article
Subject	Mathematics

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Counting Claw-Free Cubic Graphs