Contents

Hub Cover Pebbling Number

A. Lourdusamy1, F. Joy Beaula2, F. Patrick3
1St. Xavier’s College (Autonomous), Palayamkottai – 627 002, Tamilnadu, India
2Holy Cross College(Autonomous), Tiruchirapalli – 620 002, Tamilnadu, India
3Aadhavan College of Arts and Science, Manapparai – 621 307, Tamilnadu, India

Abstract

The hub cover pebbling number, \(h^{*}(G)\), of a graph $G$, is the least non-negative integer such that from all distributions of \(h^{*}(G)\) pebbles over the vertices of \(G\), it is possible to place at least one pebble each on every vertex of a set of vertices of a hub set for \(G\) using a sequence of pebbling move operations, each pebbling move operation removes two pebbles from a vertex and places one pebble on an adjacent vertex. Here we compute the hub cover pebbling number for wheel related graphs.

Keywords: Pebbling number, Cover pebbling number, Hub set