*Arthur Benjamin, Gary Chartrand, and Ping Zhang*

- Published in print:
- 2017
- Published Online:
- May 2018
- ISBN:
- 9780691175638
- eISBN:
- 9781400852000
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691175638.003.0003
- Subject:
- Mathematics, Applied Mathematics

This chapter considers distance in graphs, first by providing an overview of some fundamental concepts in graph theory. In particular, it discusses connected graphs, cut-vertex and bridge, and ...
More

This chapter considers distance in graphs, first by providing an overview of some fundamental concepts in graph theory. In particular, it discusses connected graphs, cut-vertex and bridge, and bipartite graphs. It then addresses questions of the distance between locations in a graph and those locations that are far from or close to a given location. It also looks at dominating sets in graphs, focusing on the Five Queens Problem/Puzzle and the Lights Out Puzzle, before concluding with an analysis of the rather humorous concept of Erdős numbers, conceptualized by Hungarian mathematician Paul Erdős. According to this concept, for each mathematician A, the Erdős number of A is the distance from A to Erdős in the collaboration graph. Consequently, Erdős is the only mathematician with the Erdős number 0, whereas any mathematician who has coauthored a paper with Erdős has Erdős number 1.Less

This chapter considers distance in graphs, first by providing an overview of some fundamental concepts in graph theory. In particular, it discusses connected graphs, cut-vertex and bridge, and bipartite graphs. It then addresses questions of the distance between locations in a graph and those locations that are far from or close to a given location. It also looks at dominating sets in graphs, focusing on the Five Queens Problem/Puzzle and the Lights Out Puzzle, before concluding with an analysis of the rather humorous concept of Erdős numbers, conceptualized by Hungarian mathematician Paul Erdős. According to this concept, for each mathematician *A*, the Erdős number of *A* is the distance from *A* to Erdős in the collaboration graph. Consequently, Erdős is the only mathematician with the Erdős number 0, whereas any mathematician who has coauthored a paper with Erdős has Erdős number 1.

*Péter Érdi*

- Published in print:
- 2019
- Published Online:
- September 2019
- ISBN:
- 9780190935467
- eISBN:
- 9780190935498
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780190935467.003.0002
- Subject:
- Psychology, Social Psychology

In this chapter, four basic concepts—comparison, ranking, rating, and lists—are introduced, and a number of questions are discussed. Why do we compare ourselves with others? Is comparison the “thief ...
More

In this chapter, four basic concepts—comparison, ranking, rating, and lists—are introduced, and a number of questions are discussed. Why do we compare ourselves with others? Is comparison the “thief of joy” or the driving force toward future successes? Are we born with the desire to compare ourselves with others, or do we learn in childhood that we should demonstrate that we are better or stronger than others? Is it true that “the grass is always greener on the other side of the fence”? How are ratings of graduate school applicants prepared? How do we rate our pain in a medical office? Why do we have the top-10 mania, and why do we love listicles? Ranking of mathematicians and the rating of chess players are used to illustrate the main concepts.Less

In this chapter, four basic concepts—comparison, ranking, rating, and lists—are introduced, and a number of questions are discussed. Why do we compare ourselves with others? Is comparison the “thief of joy” or the driving force toward future successes? Are we born with the desire to compare ourselves with others, or do we learn in childhood that we should demonstrate that we are better or stronger than others? Is it true that “the grass is always greener on the other side of the fence”? How are ratings of graduate school applicants prepared? How do we rate our pain in a medical office? Why do we have the top-10 mania, and why do we love listicles? Ranking of mathematicians and the rating of chess players are used to illustrate the main concepts.