Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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MONOPHONIC PEBBLING NUMBER OF SOME NETWORK-RELATED GRAPHS

  • Received : 2023.05.01
  • Accepted : 2023.11.28
  • Published : 2024.01.30
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Abstract

Chung defined a pebbling move on a graph G as the removal of two pebbles from one vertex and the addition of one pebble to an adjacent vertex. The monophonic pebbling number guarantees that a pebble can be shifted in the chordless and the longest path possible if there are any hurdles in the process of the supply chain. For a connected graph G a monophonic path between any two vertices x and y contains no chords. The monophonic pebbling number, µ(G), is the least positive integer n such that for any distribution of µ(G) pebbles it is possible to move on G allowing one pebble to be carried to any specified but arbitrary vertex using monophonic a path by a sequence of pebbling operations. The aim of this study is to find out the monophonic pebbling numbers of the sun graphs, (Cn × P2) + K1 graph, the spherical graph, the anti-prism graphs, and an n-crossed prism graph.

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Acknowledgement

We acknowledge the reviewers for their valuable suggestions to improve this article and also the editors team for their prompt reply.

References

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