Document Type
Article
Department/Program
Mathematics
Journal Title
Electronic Journal of Combinatorics
Pub Date
2009
Volume
16
Issue
1
Abstract
Given a graph G, an identifying code D subset of V(G) is a vertex set such that for any two distinct vertices v(1), v(2) is an element of V(G), the sets N[v(1)] boolean AND D and N[v(2)] boolean AND D are distinct and nonempty (here N[v] denotes a vertex v and its neighbors). We study the case when G is the infinite hexagonal grid H.Cohen et.al. constructed two identifying codes for H with density 3/7 and proved that any identifying code for H must have density at least 16/39 approximate to 0.410256. Both their upper and lower bounds were best known until now. Here we prove a lower bound of 12/29 approximate to 0.413793.
Recommended Citation
Cranston, Daniel W.; Cranston, Daniel W.; and Yu, Gexin, A New Lower Bound on the Density of Vertex Identifying Codes for the Infinite Hexagonal Grid (2009). Electronic Journal of Combinatorics, 16(1).
https://scholarworks.wm.edu/aspubs/1121
