The vertex-cover polynomial of a graph
نویسندگان
چکیده
In this paper we de1ne the vertex-cover polynomial (G; ) for a graph G. The coe2cient of r in this polynomial is the number of vertex covers V ′ of G with |V ′|= r. We develop a method to calculate (G; ). Motivated by a problem in biological systematics, we also consider the mappings f from {1; 2; : : : ; m} into the vertex set V (G) of a graph G, subject to f−1(x) ∪ f−1(y) = ∅ for every edge xy in G. Let F(G;m) be the number of such mappings f. We show that F(G;m) can be determined from (G; ). c © 2002 Elsevier Science B.V. All rights reserved.
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 250 شماره
صفحات -
تاریخ انتشار 2002