Recursive Formulas for Beans Functions of Graphs

Authors

Kengo Enami, Yokohama National UniversityFollow
Seiya Negami, Yokohama National UniversityFollow

Abstract

In this paper, we regard each edge of a connected graph G as a line segment having a unit length, and focus on not only the "vertices" but also any "point" lying along such a line segment. So we can define the distance between two points on G as the length of a shortest curve joining them along G. The beans function B_G(x) of a connected graph G is defined as the maximum number of points on G such that any pair of points have distance at least x>0. We shall show a recursive formula for B_G(x) which enables us to determine the value of B_G(x) for all x > 1 by evaluating it only for 1/2 < x ≤ 1 . As applications of this recursive formula, we shall propose an algorithm for computing B_G(x) for a given value of x ≤ 1, and determine the beans functions of the complete graphs K_n.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

Recommended Citation

Enami, Kengo and Negami, Seiya (2020) "Recursive Formulas for Beans Functions of Graphs," Theory and Applications of Graphs: Vol. 7: Iss. 1, Article 3.
DOI: 10.20429/tag.2020.070103
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol7/iss1/3