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On counting
limited outdegree grid digraphs and greatest increase grid
digraphs
Joshua Chester, Linnea Edlin, Jonah Galeota-Sprung, Bradley Isom, Alexander Moore, Virginia Perkins, A. Malcolm Campbell, Todd T. Eckdahl, Laurie J. Heyer and Jeffrey L. Poet
Vol. 9 (2016), No. 2, 211–221
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Abstract |
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In this paper, we introduce two special classes of digraphs. A limited outdegree grid (LOG) directed graph is a digraph derived from an grid graph by removing some edges and replacing some edges with arcs such that no vertex has outdegree greater than 1. A greatest increase grid (GIG) directed graph is a LOG digraph whose vertices can be labeled with distinct labels such that each arc represents the direction of greatest increase in the underlying grid graph. We enumerate both GIG and LOG digraphs for the case. |
Keywords
graph, directed graph, greatest increase grid graph,
limited outdegree grid graph, discrete gradient ascent,
enumeration
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Mathematical Subject Classification 2010
Primary: 05C20, 05C30
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Milestones
Published: 2 March 2016
Communicated by Ronald Gould
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Authors |
| Joshua Chester | |
| Department of Mathematics University of Oklahoma Norman, OK 73069 United States |
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| Linnea Edlin | |
| Department of Computer Science,
Mathematics, and Physics Missouri Western State University Saint Joseph, MO 64507 United States |
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| Jonah Galeota-Sprung | |
| Department of Mathematics Davidson College Davidson, NC 28035 United States |
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| Bradley Isom | |
| Department of Mathematics University of Kansas Lawrence, KS 66045 United States |
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| Alexander Moore | |
| Department of Chemistry University of Illinois at Urbana–Champaign Urbana, IL 61801 United States |
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| Virginia Perkins | |
| Department of Computer Science,
Mathematics, and Physics Missouri Western State University Saint Joseph, MO 64507 United States |
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| A. Malcolm Campbell | |
| Department of Biology Davidson College Davidson, NC 28035 United States |
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| Todd T. Eckdahl | |
| Department of Biology Missouri Western State University Saint Joseph, MO 64507 United States |
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| Laurie J. Heyer | |
| Department of Mathematics Davidson College Davidson, NC 28035 United States |
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| Jeffrey L. Poet | |
| Department of Computer Science,
Mathematics, and Physics Missouri Western State University Saint Joseph, MO 64507 United States |
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