  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 at a neighbouring vertex. The vertex cover set, $D_{vc}$ for graph
$G$ is the subset of $V(G)$ such that every edge in $G$ has at least one end in
$D_{vc}$. A detour monophonic path is considered to be a longest chordless path
between two non adjacent vertices $x$ and $y$. A detour monophonic vertex cover
pebbling number, ${\mu}_{vc}(G),$ is a minimum number of pebbles required to
cover all the vertices of the vertex cover set of $G$ with at least one pebble
each on them after the transformation of pebbles by using detour monophonic
paths. We determine the detour monophonic vertex cover pebbling number (DMVCPN)
of the cycle, path, fan, and wheel graphs.
