Physical Sciences and Mathematics Commons^™

Recursive Formulas For Beans Functions Of Graphs, Kengo Enami, Seiya Negami

Theory and Applications of Graphs

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 …