It is shown that the molecular symmetry groups can be obtained as the automorphism groups of edge-weighted Euclidean graphs. Graph theory provides an elegant and natural representation of molecular symmetry. The resulting group expressed in terms of permutations is isomorphic to the permutation-inversion group of Longuet-Higgins or the permutational subgroup in case inversion operations do not ...

We survey the main theoretical aspects of models for Mobile Ad Hoc Networks (MANETs). We present theoretical characterizations of mobile network structural properties, different dynamic graph models of MANETs, and finally we give detailed summaries of a few selected articles. In particular, we focus on articles dealing with connectivity of mobile networks, and on articles which show that mobili...

We introduce the index i(v) = 1− χ(S−(v)) for critical points of a locally injective function f on the vertex set V of a simple graph G = (V,E). Here S−(v) = {w ∈ S(v) | f(w) − f(v) < 0 } is the subgraph of the unit sphere S(v) generated by the vertices {w ∈ V | (v, w) ∈ E }. We prove that the sum ∑ v∈V i(v) of the indices always is equal to the Euler characteristic χ(G) of the graph G. This is...

This paper extends the notion of slicing, which was originally proposed and studied for sequential programs, to concurrent programs and presents a graph-theoretical approach to slicing concurrent programs. In addition to the usual control and data dependences proposed and studied for sequential programs, the paper introduces three new types of primary program dependences in concurrent programs,...

We prove a discrete Gauss-Bonnet-Chern theorem ∑ g∈V K(g) = χ(G) for finite graphs G = (V,E), where V is the vertex set and E is the edge set of the graph. The dimension of the graph, the local curvature form K and the Euler characteristic are all defined graph theoretically.

This paper provides improved time delay-dependent stability criteria for multi-input and multi-output (MIMO) network control systems (NCSs) with nonlinear perturbations. Without the stability assumption on the neutral operator after the descriptor approach, the new proposed stability theory is less conservative than the existing stability condition. Theoretical proof is given in this paper to d...

We study linear variable coeecient control problems in descriptor form. Based on a behaviour approach and the general theory for linear diierential algebraic systems we give the theoretical analysis and describe numerically stable methods to determine the structural properties of the system like solvability, regularity, model consistency and redundancy. We also discuss regularization via feedback.

The bit permutation networks (BPNs), proposed by Chang, Hwang and Tong (Networks, 33 (1999) 261-267), are a class of digraphs which include the underlying topological structure of almost all the commonly used switching networks or sorting networks. Many problems about BPNs have been intensively studied. Our work here is to present several graph theoretical characterizations of BPNs, which can b...

This thesis is situated in the field of combinatorial optimization. More specifically, we focus on solution methods for solving a number of graphtheoretical optimization problems. First we give a short introduction to the field of integer programming and state of the art solution techniques. The remainder of this thesis can be roughly split into two parts. The first part is dedicated to the pro...

The rapid development of high throughput experimental techniques has resulted in a growing diversity of genomic datasets being produced and requiring analysis. Therefore, it is increasingly being recognized that we can gain deeper understanding about underlying biology by combining the insights obtained from multiple, diverse datasets. Thus we propose a novel scalable computational approach to ...