Descriptive Complexity, Canonisation, and Denable Graph Structure eory

Martin Grohe Descriptive Complexity , Canonisation , and Definable Graph Structure Theory

On Symmetry of Some Nano Structures

It is necessary to generate the automorphism group of a chemical graph in computer-aided structure elucidation. An Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix M = [dij], where for i≠j, dij is the Euclidean distance between the nuclei i and j. In this matrix dii can be taken as zero if all the nuclei are equivalent. Otherwise, one may introduce...

On the Computational Complexity of the Domination Game

The domination game is played on an arbitrary graph $G$ by two players, Dominator and Staller. It is known that verifying whether the game domination number of a graph is bounded by a given integer $k$ is PSPACE-complete. On the other hand, it is showed in this paper that the problem can be solved for a graph $G$ in $mathcal O(Delta(G)cdot |V(G)|^k)$ time. In the special case when $k=3$ and the...

The Descriptive Complexity of the Reachability Problem As a Function of Different Graph Parameters

The reachability problem for graphs cannot be described, in the sense of descriptive complexity theory, using a single first-order formula. This is true both for directed and undirected graphs, both in the finite and infinite. However, if we restrict ourselves to graphs in which a certain graph parameter is fixed to a certain value, first-order formulas often suffice. A trivial example are grap...

Sampling from social networks’s graph based on topological properties and bee colony algorithm

In recent years, the sampling problem in massive graphs of social networks has attracted much attention for fast analyzing a small and good sample instead of a huge network. Many algorithms have been proposed for sampling of social network’ graph. The purpose of these algorithms is to create a sample that is approximately similar to the original network’s graph in terms of properties such as de...