Monophonic pebbling number of some families of cycles

Abstract

Let [Formula: see text] be a simple connected graph. A configuration of pebbles is a function from [Formula: see text] to a set of integers. Consider a configuration of pebbles on [Formula: see text]. A pebbling move consists of removing two pebbles off a vertex and placing one on an adjacent vertex. The monophonic pebbling number of [Formula: see text] is the smallest integer [Formula: see text] from which we can put one pebble to a target using monophonic path through pebbling moves. The monophonic [Formula: see text]-pebbling number of [Formula: see text] is the smallest positive integer [Formula: see text] such that from any configuration of [Formula: see text] pebbles we can put [Formula: see text] pebbles on a target using monophonic path. Here we discuss these concepts for families of cycles.