Information Theory and Reliable Communication

A graph labeling is an assignment of integers to the vertices or edges, or both, subject to certain conditions. Graph labelings were first introduced in the late 1960s. In the intervening years dozens of graph labelings techniques have been studied in over 1000 papers. Finding out what has been done for any particular kind of labeling and keeping up with new discoveries is difficult because of the sheer number of papers and because many of the papers have appeared in journals that are not widely available. In this survey I have collected everything I could find on graph labeling. For the convenience of the reader the survey includes a detailed table of contents and index.

/pdf/a-dynamic-survey-of-graph-labeling-198znmwxtq.pdf

A Dynamic Survey of Graph Labeling

A graph is just a bunch of points with lines between some of them, like a map of cities linked by roads. A rather simple notion. Nevertheless, the theory of graphs has broad and important applications, because so many things can be modeled by graphs. For example, planar graphs — graphs in which none of the lines cross are— important in designing computer chips and other electronic circuits. Also, various puzzles and games are solved easily if a little graph theory is applied.

A Theory of Graphs

The general Randic index Rα(G) of a (chemical) graph G, is defined as the sum of the weights (d(u)d(v))α of all edges uv of G, where d(u) denotes the degree of a vertex u in G and α an arbitrary real number, which is called the Randic index or connectivity index (or branching index) for α = −1/2 proposed by Milan Randic in 1975. The paper outlines the results known for the (general) Randic index of (chemical) graphs. Some very new results are released. We classify the results into the following categories: extremal values and extremal graphs of Randic index, general Randic index, zeroth-order general Randic index, higher-order Randic index. A few conjectures and open problems are mentioned.

A Survey on the Randic Index

We present AutoTutor and Affective AutoTutor as examples of innovative 21st century interactive intelligent systems that promote learning and engagement. AutoTutor is an intelligent tutoring system that helps students compose explanations of difficult concepts in Newtonian physics and enhances computer literacy and critical thinking by interacting with them in natural language with adaptive dialog moves similar to those of human tutors. AutoTutor constructs a cognitive model of students' knowledge levels by analyzing the text of their typed or spoken responses to its questions. The model is used to dynamically tailor the interaction toward individual students' zones of proximal development. Affective AutoTutor takes the individualized instruction and human-like interactivity to a new level by automatically detecting and responding to students' emotional states in addition to their cognitive states. Over 20 controlled experiments comparing AutoTutor with ecological and experimental controls such reading a textbook have consistently yielded learning improvements of approximately one letter grade after brief 30--60-minute interactions. Furthermore, Affective AutoTutor shows even more dramatic improvements in learning than the original AutoTutor system, particularly for struggling students with low domain knowledge. In addition to providing a detailed description of the implementation and evaluation of AutoTutor and Affective AutoTutor, we also discuss new and exciting technologies motivated by AutoTutor such as AutoTutor-Lite, Operation ARIES, GuruTutor, DeepTutor, MetaTutor, and AutoMentor. We conclude this article with our vision for future work on interactive and engaging intelligent tutoring systems.

https://www.ida.liu.se/divisions/hcs/seminars/cogsciseminars/Papers/dmello-TiiS12.pdf

AutoTutor and affective autotutor: Learning by talking with cognitively and emotionally intelligent computers that talk back

Wiener index versus maximum degree in trees

Irreversible conversion of graphs

http://www.or.uni-bonn.de/home/vygen/files/gendijk.pdf

A generalization of Dijkstra's shortest path algorithm with applications to VLSI routing

The band-, tree-, and clique-width are of primary importance in algorithmic graph theory due to the fact that many problems that are NP-hard for general graphs can be solved in polynomial time when restricted to graphs where one of these parameters is bounded. It is known that for any fixed $\Delta \geq 3$, all three parameters are unbounded for graphs with vertex degree at most $\Delta$. In this paper, we distinguish representative subclasses of graphs with bounded vertex degree that have bounded band-, tree-, or clique-width. Our proofs are constructive and lead to efficient algorithms for a variety of NP-hard graph problems when restricted to those classes.

Dieter Rautenbach

Papers

Wiener index versus maximum degree in trees

Irreversible conversion of graphs

A generalization of Dijkstra's shortest path algorithm with applications to VLSI routing

On the Band-, Tree-, and Clique-Width of Graphs with Bounded Vertex Degree

Some results on graphs without long induced paths