Vol. 9, No. 2, 2016

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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
Abstract

In this paper, we introduce two special classes of digraphs. A limited outdegree grid (LOG) directed graph is a digraph derived from an n × n 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 3×3 case.

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Keywords
graph, directed graph, greatest increase grid graph, limited outdegree grid graph, discrete gradient ascent, enumeration
Mathematical Subject Classification 2010
Primary: 05C20, 05C30
Milestones
Published: 2 March 2016

Communicated by Ronald Gould
Authors
Joshua Chester
Department of Mathematics
University of Oklahoma
Norman, OK 73069
United States
Linnea Edlin
Department of Computer Science, Mathematics, and Physics
Missouri Western State University
Saint Joseph, MO 64507
United States
Jonah Galeota-Sprung
Department of Mathematics
Davidson College
Davidson, NC 28035
United States
Bradley Isom
Department of Mathematics
University of Kansas
Lawrence, KS 66045
United States
Alexander Moore
Department of Chemistry
University of Illinois at Urbana–Champaign
Urbana, IL 61801
United States
Virginia Perkins
Department of Computer Science, Mathematics, and Physics
Missouri Western State University
Saint Joseph, MO 64507
United States
A. Malcolm Campbell
Department of Biology
Davidson College
Davidson, NC 28035
United States
Todd T. Eckdahl
Department of Biology
Missouri Western State University
Saint Joseph, MO 64507
United States
Laurie J. Heyer
Department of Mathematics
Davidson College
Davidson, NC 28035
United States
Jeffrey L. Poet
Department of Computer Science, Mathematics, and Physics
Missouri Western State University
Saint Joseph, MO 64507
United States