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The generating function of Whitworth runs

✍ Scribed by C.J. Liu

Publisher
Elsevier Science
Year
1984
Tongue
English
Weight
715 KB
Volume
51
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis

Let G be a graph. The number of ways of selecting k vertices in G such that the subgraph induced by the k selected vertices containing 1 edges may be considered as Whitworth runs. For two arbitrary graphs Gr and G2 we show that the generating function of G1 can be written as a sum of the generating function of GZ. As an application we derive a difference equation satisfted by the generating function of a line maph and that of a cycle graph. Two independent solutions in the closed-form are found. One is equivalent to the Whitworth bracelet problem with two dors. Furthermore, a line and a cycle graph and a two-line graph have been studied.

We show that all sohuions can be written as a sum of the solutions for single-line cases.

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