Monophonic pebbling number and t-pebbling number of some graphs

Assume G is a graph with some pebbles distributed over its vertices. A pebbling move is when two pebbles are removed from one vertex, one is thrown away, and the other is moved to an adjacent vertex. The monophonic pebbling number, mu(G), of a connected graph G, is the least positive integer n such that any distribution of n pebbles on G allows one pebble to be carried to any specified but arbitrary vertex using monophonic path by a sequence of pebbling operations. The least positive integer n such that any distribution of n pebbles on G allows t pebbles to be moved to any specified but arbitrary vertex by a sequence of pebbling moves using monophonic path is the monophonic t-pebbling number mu(t)(G). The monophonic pebbling number and monophonic t-pebbling number of Jahangir graphs, paths and square of paths are determined in this study.

Automated summary

The monophonic pebbling number mu(G) is the least positive integer n such that any distribution of n pebbles on a graph G allows one pebble to be carried to any specified vertex using monophonic path by a sequence of pebbling operations. The monophonic t-pebbling number mu(t)(G) is the least positive integer n such that any distribution of n pebbles on G allows t pebbles to be moved to any specified vertex by a sequence of pebbling moves using monophonic path. This study determines the monophonic pebbling number and monophonic t-pebbling number of Jahangir graphs, paths, and square of paths.