Monophonic Cover Pebbling Number of Standard and Algebraic Graphs

A. Lourdusamy; S. Kither iammal; I. Dhivviyanandam

doi:10.26713/cma.v15i2.2625

Authors

A. Lourdusamy Department of Mathematics, St. Xavier’s College (Autonomous) (affiliated to Manonmaniam Sundaranar University), Palayamkottai 627002, Tamil Nadu, India https://orcid.org/0000-0001-5961-358X (unauthenticated)
S. Kither iammal Department of Mathematics, Jayaraj Annapackiam College for Women (affiliated to Mother Teresa Women’s University), Periyakulam 625601, Tamil Nadu, India https://orcid.org/0000-0003-3553-0848 (unauthenticated)
I. Dhivviyanandam Department of Mathematics, North Bengal St. Xavier’s College (affiliated to the University of North Bengal), Rajganj, West Bengal, India https://orcid.org/0000-0002-3805-6638 (unauthenticated)

DOI:

https://doi.org/10.26713/cma.v15i2.2625

Keywords:

Cover pebbling, Monophonic pebbling, Monophonic cover pebbling, Zero divisor, Unit graph

Abstract

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, \(\gamma_\mu(G)\), 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.

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