Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4648708 | Discrete Mathematics | 2010 | 7 Pages |
Abstract
A simple graph GG is representable in a real vector space of dimension mm, if there is an embedding of the vertex set in the vector space such that the Euclidean distance between any two distinct vertices is one of only two distinct values, αα and ββ, with distance αα if the vertices are adjacent and distance ββ otherwise. The Euclidean representation number of GG is the smallest dimension in which GG is representable. In this note, we bound the Euclidean representation number of a graph using multiplicities of the eigenvalues of the adjacency matrix. We also give an exact formula for the Euclidean representation number using the main angles of the graph.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Aidan Roy,