Abstract
It is well known that the Cartesian product of two paths, the grid Pm□Pn,m≤n, has an independent dominating set such that every vertex not in the set has exactly one neighbor in it, if and only if m=n=4 or m=2,n=2k+1. In this paper we prove that every grid Pm□Pn has an independent dominating set such that every vertex not in the set has at most two neighbors in it, and we also calculate the minimum cardinality of such sets.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have