Monophonic cover pebbling number of standard and algebraic Graphs

Authors

Keywords:

cover pebbling, monophonic pebbling, monophonic cover pebbling, zero divisor, unit graphs

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, $\gamma_\mu\left(G\right)$, is a minimum number of pebbles required to cover all the vertices of $G$ with at least one pebble each on them after the transfermation 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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Published

14-11-2024

How to Cite

Soosaimanickam, K. iammal, Arockiam, . L., & Irudayaraj, . D. (2024). Monophonic cover pebbling number of standard and algebraic Graphs. Communications in Mathematics and Applications, 15(2). Retrieved from https://rgnpublications.com/journals/index.php/cma/article/view/2625

Issue

Vol. 15 No. 2 (2024)

Section

Research Article

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