The vertex-cover polynomial of a graph

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Abstract

In this paper we define the vertex-cover polynomial y(G,t) for a graph G. The coefficient of -f in this polynomial is the number of vertex covers V' of G with W'\ =r. We develop a method to calculate y(G, r). Motivated by a problem in biological systematics, we also consider the mappings / from {1, 2,...,m} into the vertex set V(G) of a graph G, subject to /~'(.v)U f-1)-40 for every ed8e xy in G- Let F(G,m) be the number of such mappings J. We show that F(G,m) can be determined from y(G,t). ©2002 Elsevier Science B.V. All rights reserved. ».

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Dong, P. M., Hendy, M. D., Teo, K. L., & Little, C. H. C. (2002). The vertex-cover polynomial of a graph. Discrete Mathematics, 250(1–3), 71–78. https://doi.org/10.1016/S0012-365X(01)00272-2

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