Weak Convex Domination in Hypercubes

Abstract

The n-cube Qn is the graph whose vertex set is the set of all n-dimensional Boolean vectors, two vertices being joined if and only if they differ in exactly one coordinate. The n-star graph Sn is a simple graph whose vertex set is the set of all n! permutations of {1, 2, · · · , n} and two vertices α and β are adjacent if and only if α(1)≠β(1) and α(i) ≠β(i) for exactly one i, i≠ 1.
 In this paper we determine weak convex domination number for hypercubes. Also convex, weak convex, m - convex and l1-convex numbers of star and hypercube graphs are determined.