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, $\mu(G)$, 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 monophonic pebbling number of cycle graphs, fan graphs, wheel graphs, star graphs, complete graphs, middle graphs of path are being discussed.

Keywords and Phrases

Monophonic pebbling number, monophonic distance, monophonic path.

A.M.S. subject classification

05C12, 05C25, 05C38, 05C76.

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