Monophonic pebbling number and t-pebbling number of some graphs

Abstract

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, 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 The monophonic pebbling number and monophonic t-pebbling number of Jahangir graphs, paths and square of paths are determined in this study.