Year: 2025
Type: article
Abstract: Graph pebbling is a network optimization approach for the movement of resources in transit. A pebbling move in a connected graph G is defined as a distribution of pebbles on the vertices of the network, remove two pebbles from a vertex, place one pebble on one of its adjacent vertices, and discard the other pebble. The loss of one pebble in a pebbling move can be related to the packet loss in message transmission between the computers. The generalization of packet loss in this process is defined as t-pebbling. The t-pebbling number f t (G) is the least significant positive integer such that, for every distribution of f t (G) pebbles, t pebbles can be transferred to a vertex v, for every v in G, using a pebbling sequence. A graph G is said to satisfy a 2t-pebbling property if 2t pebbles can be transferred to v when the graph is distributed with 2f t (G)-q + 1 pebbles, where q is the number of vertices with at least one pebble. In this paper a lower bound for rooted product of two graphs G and H is determined and the bound is proved to be sharp when one of the graphs in the rooted product is a path, complete graph or a star. Furthermore, this paper explores some new results on pebbling in triangle free graphs. In particular, 2t-pebbling property is verified for rooted product whenever one of the graph is a Triangle free graph.
Source: Congressus Numerantium
DOI: 10.61091/cn236-03
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4413977295