The vertex-cover polynomial of a graph

The vertex-cover polynomial of a graph

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 x...

Improving Vertex Cover as a Graph Parameter

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On the Roots of Hosoya Polynomial of a Graph

Let G = (V, E) be a simple graph. Hosoya polynomial of G is d(u,v) H(G, x) = {u,v}V(G)x , where, d(u ,v) denotes the distance between vertices u and v. As is the case with other graph polynomials, such as chromatic, independence and domination polynomial, it is natural to study the roots of Hosoya polynomial of a graph. In this paper we study the roots of Hosoya polynomials of some specific g...

Graph Layout Problems Parameterized by Vertex Cover

In the framework of parameterized complexity, one of the most commonly used structural parameters is the treewidth of the input graph. The reason for this is that most natural graph problems turn out to be fixed parameter tractable when parameterized by treewidth. However, Graph Layout problems are a notable exception. In particular, no fixed parameter tractable algorithms are known for the Cut...

On Szeged Polynomial of a Graph