Pebbling of Oriented Graphs

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Pebbling of Oriented Graphs

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DeVries, Jerad S

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2017-09

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Abstract

In traditional graph pebbling a move across an edge is made by removing two pebbles from one vertex and adding one pebble to an adjacent vertex. We extend this concept to oriented graphs by subtracting three pebbles when moving against an edge orientation and two pebbles when moving with an edge orientation. The cover pebbling number of an oriented graph is the minimum number of pebbles such that given any initial placement of these pebbles we can simultaneously place a pebble on every vertex. In this paper we will look at pebblings of oriented paths.

Keywords

Pebbling

Oriented paths

Vertex

Graph pebbling

Oriented graphs

Traditional pebbling

Target pebbling

Cover pebbling

Stacking Theorem

Department of Mathematics and Statistics

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Submitted to the faculty of the Graduate School of the University of Minnesota in partial fulfillment of the requirements for the degree of Master of Science. September, 2017. Major: Mathematics and Statistics. Advisor: Dalibor Froncek. 1 computer file (PDF); vii, 38 pages, graphs

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Master's Degree Culminating Works
Master of Science in Mathematical Sciences and Master of Science in Applied and Computational Mathematics Plan B Project Papers

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DeVries, Jerad S. (2017). Pebbling of Oriented Graphs. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/190403.

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