The Geometric Index of the Wheel, Wn
Rowena Tejano Baylon
cpt@math1.msuiit.edu.ph
Affiliation
Abstract
Define the geometric index of a graph G as the smallest nonnegative integer n such that G is a unit graph in R^n. Graphs considered are finite, undirected, without loops nor multiple edges. Also, edge crossings are allowed in the figures but distinct vertices must have distinct coordinates and that the line segment joining adjacent vertices must not pass through any other vertex.
ln this paper, the geometric index mu of the wheel W_n (n = 3,4,5,...) are discovered and proven. As a consequence to the said result, the geometric indices of the graphs like the helm, the double cone, web and the octahedron were also discovered.
The results of this study may serve as stepping stones for other researchers who are interested in expanding the study of geometric index on all graphs.
© Asian Technology Conference in Mathematics, 1998. |
