Home > Journals > TAG > Vol. 7 > Iss. 1 (2020)
Article Title
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 $x \leq 1$ by evaluating it only for $1/2 < x \leq 1$. As applications of this recursive formula, we shall propose an algorithm for computing $B_G(x)$ for a given value of $x\leq 1$, and determine the beans functions of the complete graphs $K_n$.
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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
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