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A New Lower Bound on the Density of Vertex Identifying Codes for the Infinite Hexagonal Grid
Cranston, Daniel W. Cranston, Daniel W. Yu, Gexin
Cranston, Daniel W.
Cranston, Daniel W.
Yu, Gexin
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.
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2009-01-01
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A_New_Lower_Bound.pdf
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Mathematics