Rainbow Colorings in Graphs

In this thesis, we deal with rainbow colorings of graphs. We engage not with the rainbow connection number but with counting of rainbow colorings in graphs with k colors. We introduce the rainbow polynomial and prove some results for some special graph classes. Furthermore, we obtain bounds for the rainbow polynomial. In addition, we define some edge colorings related to the rainbow coloring, like the s-rainbow coloring and the 2-rainbow coloring. For this edge colorings, polynomials are defined and we prove some basic properties for this polynomials and present some formulas for the calculation in special graph classes. In addition, we consider in this thesis counting problems related to the rainbow coloring like rainbow pairs and rainbow dependent sets. We introduce polynomials for this counting problems and present some general properties and formulas for special graph classes

Structure of communication networks in electromobility and suitable reliability measures

Die vorliegende Arbeit beschäftigt sich mit der Struktur und den Komponenten in mobilen Kommunikationsnetzen. Es wird zudem herausgearbeitet, welche Kennzahlen notwendig sind, um die Verfügbarkeit und die Überlebensfähigkeit von mobilen Kommunikationsnetzen einschätzen und bewerten zu können. In diesem Zusammenhang wird zudem untersucht, welche Forschungsergebnisse bezüglich der Zuverlässigkeit in diesen Netzen zur Verfügung stehen. Der letzte Punkt, der in dieser Arbeit berücksichtigt wurde, ist die Anwendung der mobilen Kommunikationsnetze in der Praxis. Dabei wird auch die Kommunikation zwischen den Fahrzeugen beschrieben, die zukünftig eine wichtige Rolle dabei spielen soll, die Verkehrslage in Deutschland sicherer zu machen

Rainbow Colorings in Graphs

In this thesis, we deal with rainbow colorings of graphs. We engage not with the rainbow connection number but with counting of rainbow colorings in graphs with k colors. We introduce the rainbow polynomial and prove some results for some special graph classes. Furthermore, we obtain bounds for the rainbow polynomial. In addition, we define some edge colorings related to the rainbow coloring, like the s-rainbow coloring and the 2-rainbow coloring. For this edge colorings, polynomials are defined and we prove some basic properties for this polynomials and present some formulas for the calculation in special graph classes. In addition, we consider in this thesis counting problems related to the rainbow coloring like rainbow pairs and rainbow dependent sets. We introduce polynomials for this counting problems and present some general properties and formulas for special graph classes