Monophonic Cover Pebbling Number of Standard and Algebraic Graphs - Lourdusamy, A.; Kither iammal, S.; Dhivviyanandam, I. (Communications in Mathematics and Applications, 2024)
Given a connected graph \(G\) and a configuration \(D\) of pebbles on the vertices of \(G\), a pebbling transformation takes place by removing two pebbles from one vertex and placing one pebble on its adjacent vertex. A monophonic path is considered to be a longest chordless path between two vertices \(u\) and \(v\) which are not adjacent. A monophonic cover pebbling number, \(γ_μ(G)\), is a minimum number of pebbles required to cover all the vertices of \(G\) with at least one pebble each on them after the transferring of pebbles by using monophonic paths. In this paper, we determine the monophonic cover pebbling number of cycles, square of cycles, shadow graph of cycles, complete graphs, Jahangir graphs, fan graphs, zero divisor graphs and unit graphs.