The independence polynomial of a graph G is the function i(G, x) = ∑k≥0 ik xk , where ik is the number of independent sets of vertices in G of cardinality k. We prove that real roots of independence polynomials are dense in (−∞, 0], while complex roots are dense in C, even when restricting to well covered or comparability graphs. Throughout, we exploit the fact that independence polynomials are...

Resilience is a concept of rising interest in computer science and software engineering. For systems which correctness w.r.t. safety condition unachievable, fast recovery demanded. We investigate resilience problems graph transformation systems. Our main contribution the decidability two for well-structured (with strong compatibility). prove our results abstract framework transition apply them ...

The stability number α(G) of the graph G is the size of a maximum stable set of G. If sk denotes the number of stable sets of cardinality k in graph G, then I(G;x) = α(G)

We study the problem of covering graphs with trees and a graph of bounded maximum degree. By a classical theorem of Nash-Williams, every planar graph can be covered by three trees. We show that every planar graph can be covered by two trees and a forest, and the maximum degree of the forest is at most 8. Stronger results are obtained for some special classes of planar graphs.

Laser range imaging is an upcoming data source for many fields of research. Although many methods are proposed for finding surfaces and classifying points, finding the bounds of these surfaces is still a difficult problem. We propose a method for finding, in a point set of size n, a rectangle that contains a predefined subset of the points and none of the other points in O(n log n) time. Furthe...

A graph G is well-covered provided each maximal independent set of vertices has the same cardinality. The term sk of the independence sequence (s0, s1, . . . , sα) equals the number of independent k-sets of vertices of G. We investigate constraints on the linear orderings of the terms of the independence sequence of well-covered graphs. In particular, we provide a counterexample to the recent u...

The center (periphery) of a graph is the set of vertices with minimum (maximum) eccentricity. In this paper, the structure of centers and peripheries of some classes of composite graphs are determined. The relations between eccentricity, radius and diameter of such composite graphs are also investigated. As an application we determine the center and periphery of some chemical graphs such as nan...

Little [12] showed that, in a certain sense, the only minimal non-Pfaffian bipartite matching covered graph is the brace K3,3. Using a stronger notion of minimality than the one used by Little, we show that every minimal nonPfaffian brick G contains two disjoint odd cycles C1 and C2 such that the subgraph G − V (C1 ∪ C2) has a perfect matching. This implies that the only minimal non-Pfaffian so...