Weak Convex Domination in Hypercubes

SV Padmavathi; K Krishnan

doi:10.34293/sijash.v8iS1-May.4507

SV Padmavathi Assistant Professor of Mathematics, Ramanujan Research Center in Mathematics, Saraswathi Narayanan College, Madurai, Tamil Nadu, India
K Krishnan Vice- Principal and Associate Professor of Mathematics, Saraswathi Narayanan College, Madurai, Tamil Nadu, India

DOI: https://doi.org/10.34293/sijash.v8iS1-May.4507

Keywords: Convexity number, Weak convexity number, Weak convex domination, m - convexity number, l1 - convexity number

Abstract

The n-cube Q_nis 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 S_nis 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.