@jeppiaararts.in
Assistant professor, Department of Mathematics
Jeppiaar College of Arts and Science, Padur, Chennai, Tamil
Graph Pebbling
Graph theory
Number theory
Computational mathematics
Scopus Publications
J. Jenifer Steffi and A. Lourdusamy
AIP Publishing
Given a distribution of pebbles on the vertices of a connected graph G, a pebbling move consists of taking two pebbles off one vertex and placing one on an adjacent vertex. The pebbling number f (G) of a connected graph G is the smallest positive integer such that every distribution of f (G) pebbles on the vertices of G, we can move a pebble to any target vertex. The t-pebbling number ft (G) of a connected graph G is the smallest positive integer such that every distribution of ft (G) pebbles on the vertices of G, we can move t pebbles to any target vertex by a sequence of pebbling moves. Graham conjectured that for any connected graph G and H, f (G × H) ≤ f (G) f (H). Lourdusamy further conjectured that ft (G × H) ≤ f (G) ft (H) for any positive integer t. In this paper, we show that Lourdusamy’s Conjecture is true when G is a zig-zag chain graph of n copies of even cycles and H is a graph having 2t- pebbling property.
A. Lourdusamy and J. Jenifer Steffi
Universidad Catolica del Norte - Chile
Given a distribution of pebbles on the vertices of a connected graph G, a pebbling move on G consists of removing two pebbles from one vertex and placing one pebble on an adjacent vertex. The pebbling number of G, f (G), is the least n such that any distribution of n pebbles on G allows one pebble to be reached to any specified, but an arbitrary vertex. Similarly, the t−pebbling number of G, ft(G), is the least m such that from any distribution of m pebbles, we can move t pebbles to any specified, but an arbitrary vertex. In this paper, we determine the pebbling number, and the t−pebbling number of the zigzag chain graph of n copies of odd cycles.