Joseph A Gallian

Joseph A Gallian
University of Minnesota, Duluth | UMD · Department of Mathematics & Statistics

Doctor of Philosophy

About

137
Publications
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5,537
Citations

Publications

Publications (137)
Article
We review the 75-year history of the world's foremost college-level mathematics competition. Evidence is provided to support the assertion that exceptional performance in premier secondary-school-level and college-level mathematics competitions correlates well with an exceptional research career in mathematics.
Article
Directions for mathematics research experience for undergraduates edited by Peterson Mark A. and Rubinstein Yanir A. , pp 252, $78.00 (hard), ISBN 978-9-81463-031-3, also available as e-book, World Scientific (2016). - Volume 100 Issue 549 - Joseph A. Gallian
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A graph G with q edges is said to be harmonious if there is an injection f from the vertices of G to the group of integers modulo q such that when each edge xy is assigned the label f(x)+f(y)(modq), the resulting edge labels are distinct. If G is a tree, exactly one label may be used on two vertices. Over the years, many variations of harmonious la...
Article
Full-text available
A graph G with q edges is said to be harmonious if there is an injection f from the vertices of G to the group of integers modulo q such that when each edge xy is assigned the label f(x)+f(y)(modq), the resulting edge labels are distinct. If G is a tree, exactly one label may be used on two vertices. Over the years, many variations of harmonious la...
Article
Full-text available
We provide a historical report of the undergraduate poster session at the annual joint meetings of the American Mathematical Society and the Mathematical Association of America from its inception in 1991 until 2013. We also provide data on the number of undergraduates attending the joint meetings and the number giving talks.
Article
A graph G with q edges is said to be harmonious if there is an injection f from the vertices of G to the group of integers modulo q such that when each edge xy is assigned the label f(x) + f(y) (mod q), the resulting edge labels are distinct. When G is a tree, exactly one label may be used on two vertices. Recently two variants of harmonious labeli...
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See DS 6 at https://www.combinatorics.org/ojs/index.php/eljc/issue/view/Surveys
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Full-text available
In this article I trace my involvement with graph labeling for the past 25 years. I provide some statistical information about the growth in interest in graph labeling and some open problems that I believe are accessible.
Article
This book is an eclectic compendium of the essays solicited for the 2010 Mathematics Awareness Month web page on the theme of Mathematics and Sports. In keeping with the goal of promoting mathematics awareness to a broad audience, all of the articles are accessible to college level mathematics students and many are accessible to the general public....
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https://www.combinatorics.org/ojs/index.php/eljc/article/view/DS6/pdf
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The connection, if any, between gender (or other demographic factors) and mathematical skills has been much discussed in the popular and scientific press. In this study, the authors investigate ultrahigh-level mathematical ability by looking at top tier mathematics competitions and find that girls and boys do equally well.
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Full-text available
A vertex labeling of a graph G is an assignment f of labels to the vertices of G that induces for each edge xy a label depending on the vertex labels f(x) and f(y). The two best known labeling methods are called graceful and harmonious labelings. A function f is called a graceful labeling of a graph G with q edges if f is an injection from the vert...
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This paper describes Project NExT (New Experiences in Teaching), a professional development program for new or recent Ph.D.s in the mathematical sciences. The program consists of workshops and short courses on teaching, establishing a research program, involving undergraduates in research, grant writing, and balancing teaching and research. An intr...
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The use of check digits with identification numbers for error detection is now standard practice. Notable exceptions such as social security numbers, telephone numbers and serial numbers on currency predate computers. Despite their ubiquity and utility, few people are knowledgeable about the myriad of check digit schemes in use by businesses. In th...
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Full-text available
Cayley graphs arise naturally in computer science, in the study of word-hyperbolic groups and automatic groups, in change-ringing, in creating Escher-like repeating patterns in the hyperbolic plane, and in combinatorial designs. Moreover, Babai has shown that all graphs can be realized as an induced subgraph of a Cayley graph of any sufficiently la...
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The above theorems are sufficient to demonstrate the existence of antisymmetric mappings for all non-Abelian group of order less than 36, except for the group a, b\a 3 =b 8 =e, ab =ba 2> of order 24, and this group can be shown to have one. On the basis of our results, and the fact that we have no conditions on a non-Abelian group that would elimin...
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Full-text available
In this paper we survey many of the variations of graceful and harmonious labeling methods that have been introduced and summarize much of what is known about each kind.
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Discussed are the mathematical methods for detecting a variety of common error patterns within the bar-coded identification numbers utilized in conjunction with scanning devices. Schemes for the use of check digits are examined that ensure conditions for detecting errors of specific types, including single digit error, transposition error, twin err...
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In this paper we introduce a method of sequencing the elements of a finite group that gives rise to a complete mapping of the group. Our definition was motivated by the concept of a harmonious graph invented by Graham and Sloane. Our concept has several connections to graph theory and as an application we complete the characterization of elegant cy...
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Full-text available
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In the excellent film “Let Us Teach Guessing,” Pólya (1966) poses a geometry problem to a class and asks the students to guess the solution. Without saying whether these guesses are right, he proceeds to lead the class step by step to the point where they can guess the correct solution of the problem. As Poly a has said, “Everything is just a guess...
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Full-text available
In this paper we organize and summarize much of the work done on graceful and harmonious labelings of graphs. Many open problems and conjectures are included.

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