Identifying codes for infinite triangular grids with a finite number of rows

A set C⊂V(G) is an identifying code in a graph G if for all v∈V(G), C[v]≠∅, and for all distinct u,v∈V(G), C[u]≠C[v], where C[v]=N[v]∩C and N[v] denotes the closed neighborhood of v in G. The minimum density of an identifying code in G is denoted by d∗(G). Given a positive integer k, let Tk be the triangular grid with k rows. In this paper, we prove that d∗(T1)=d∗(T2)=1∕2, d∗(T3)=d∗(T4)=1∕3, d∗(T5)=3∕10, d∗(T6)=1∕3 and d∗(Tk)=1∕4+1∕(4k) for every k≥7 odd. Moreover, we prove that 1∕4+1∕(4k)≤d∗(Tk)≤1∕4+1∕(2k) for every k≥8 even. We conjecture that d∗(Tk)=1∕4+1∕(2k) for every k≥8 even.