1Detour monophonic vertex cover pebbling number (DMVCPN) of some standard graphs

Let G be a connected graph with vertex set V ( G ) and edge set E ( G ) . Pebbling shift is a deletion of two pebbles from a vertex and a placement of one pebble to a neighboring vertex. The vertex cover set D v c for graph G is the subset of V ( G ) such that every edge in G has at least one end in D v c . A detour monophonic path is considered to be a longest chordless path between two nonadjacent vertices x and y . A detour monophonic vertex cover pebbling number μ v c ( G ) is a minimum number of pebbles required to cover all the vertices of the vertex cover set of G with at least one pebble on each after the transformation of pebbles by using detour monophonic paths. We determine the detour monophonic vertex cover pebbling number (DMVCPN) of Cycle, Path, Fan, and Wheel graphs.