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Career Summary

Biography

I feel my research output has been a productive one. I am grateful for having had the opportunity to have been involved in so much interesting research work with so many helpful colleagues.

Qualifications

  • PhD, University of Newcastle, 04/03/2005
  • Bachelor of Science (Honours), Dalhousie University - Canada
  • Master of Philosophy, University of Waterloo
  • Master of Arts, Dalhousie University - Canada

Research

Research keywords

  • Graph Theory
  • Number Theory

Research expertise

Graph labelings, in particular magic and anti-magic labelings. Related combinatorial arrays such as sparse magic and anti-magic squares (collaboration with W. D. Wallis, SIU and J. S. Kimberley and M. Miller, U of Newcastle).

Diophantine problems - problems in algebra and geometry that give rise to diophantine equations, especially elliptic curves. These include characterizing polynomials some or all of whose derivatives split into linear factors over the rational integers, and characterizing rational-sided polygons or polyhedra which have rational areas, volume or other parameters. (collaboration with R. H. Buchholz, DSTO)

Various problems in graph theory: the structure of the subgraph poset and universal graphs, graphs saturated with respect to triangles or other subgraphs (collaboration with R. B. Eggleton, ISU).

Linear algebras with various properties, including homogeneous algebras with a view to describing the structure of various classes, e.g. anti-commutative algebras, nilpotent algebras or quasi-division algebras; spaces of matrices of fixed rank or nilindex. (collaboration with L.G. Sweet, U of PEI)

Fields of Research

CodeDescriptionPercentage
010199Pure Mathematics Not Elsewhere Classified80
080299Computation Theory And Mathematics Not Elsewhere Classified15
010299Applied Mathematics Not Elsewhere Classified5

Memberships

Learned Academy.

  • member - American Mathematical Society
  • member - Australian Mathematical Society
  • member - Canadian Mathematical Society

Awards

Research Award.

1983Faculty Merit Award
University of Prince Edwars Island (Canada)
Award for outstanding research as well as teaching.

Invitations

2002 Connect conference
DIMACS at Rutgers, United States (Conference Presentation - non published.)
2002

Teaching

Teaching keywords

  • Mathematics

Teaching expertise

40+ years of teaching a wide variety of mathematics courses at university level

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Highlighted Publications

For publications that are currently unpublished or in-press, details are shown in italics.

YearCitationAltmetricsLink
2006Chisholm CR, MacDougall JA, 'Rational and Heron tetrahedra', Journal of Number Theory, 121 153-185 (2006) [C1]
2002Eggleton RB, MacDougall JA, 'Minimally triangle-saturated graphs: adjoining a single vertex', Australasian Journal of Combinatorics, 25 263-278 (2002) [C1]
2002Sweet LG, MacDougall JA, 'A decomposition theorem for homogeneous algebras', Journal of the Australian Mathematical Society, 72 47-56 (2002) [C1]
2008Buchholz RH, MacDougall JA, 'Cyclic polygons with rational sides and area', Journal of Number Theory, 128 17-48 (2008) [C1]
2000MacDougall JA, Buchholz RH, 'When Newton met Diophantus: A Study of Rational-Derived Polynomials and Their Extension to Quadratic Fields', Journal of Number Theory, 81 210-233 (2000) [C1]

Publications

For publications that are currently unpublished or in-press, details are shown in italics.

Click on a category title below to expand the list of citations for that specific category.

Journal article (51 outputs)

YearCitationAltmetricsLink
2012Eggleton RB, Kimberley JS, MacDougall JA, 'Runs of integers with equally many distinct prime factors', Bulletin of the Institute of Combinatorics and its Applications, 64 30-38 (2012) [C1]
2012MacDonald GW, MacDougall JA, Sweet LG, 'On the dimension of linear spaces of nilpotent matrices', Linear Algebra and Its Applications, 436 2210-2230 (2012) [C1]
2012Kimberley JS, MacDougall JA, 'Mutation of vertex-magic regular graphs', Journal of Combinatorial Mathematics and Combinatorial Computing, 82 157-177 (2012) [C1]
2012Gray ID, MacDougall JA, 'Vertex-magic labeling of regular graphs: Disjoint unions and assemblages', Discrete Applied Mathematics, 160 1114-1125 (2012) [C1]
2012MacDougall JA, Sweet LG, 'Rational homogeneous algebras', Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques, 55 351-354 (2012) [C1]
2011Kimberley JS, MacDougall JA, 'All regular graphs of small odd order are vertex-magic', Australasian Journal of Combinatorics, 51 175-199 (2011) [C1]
2010Mohr SH, MacDougall JA, 'Integral Trees of Diameter 4', AKCE International Journal of Graphs and Combinatorics, 7 171-188 (2010) [C1]
2010Gray ID, MacDougall JA, 'Vertex-magic labelling of non-regular graphs', Australasian Journal of Combinatorics, 46 173-183 (2010) [C1]
2009Gray ID, MacDougall JA, 'Vertex-magic labelings of regular graphs II', Discrete Mathematics, 309 5986-5999 (2009) [C1]
2009Gray ID, MacDougall JA, 'Vertex-magic labelings: Mutations', Australasian Journal of Combinatorics, 45 189-206 (2009) [C1]
2009Eggleton RB, Adams P, MacDougall JA, 'Graphs which are linked structures', Congressus Numerantium, 199 75-88 (2009) [C1]
2009Adams P, Eggleton RB, MacDougall JA, 'Graphs which are linked cycles', Congressus Numerantium, 195 75-83 (2009) [C1]
2009Sweet LG, MacDougall JA, 'The maximum dimension of a subspace of nilpotent matrices of index 2', Linear Algebra and Its Applications, 431 1116-1124 (2009) [C1]
2008Chisholm CR, MacDougall JA, 'Rational tetrahedra with edges in geometric progression', Journal of Number Theory, 128 251-262 (2008) [C1]
2008Eggleston RB, MacDougall JA, 'Consecutive integers with equally many principal divisors', Mathematics Magazine, 81 235-248 (2008) [C1]
2008Buchholz RH, MacDougall JA, 'Cyclic polygons with rational sides and area', Journal of Number Theory, 128 17-48 (2008) [C1]
2008MacDougall JA, Wallis WD, 'Strong edge-magic graphs of maximum size', Discrete Mathematics, 308 2756-2763 (2008) [C1]
2006Gray ID, MacDougall JA, 'Sparse anti-magic squares and vertex-magic labelings of bipartite graphs', Discrete Mathematics, 306 2878-2892 (2006) [C1]
2006Adams PD, Eggleton RG, MacDougall JA, 'Graphs with a given degree sequence', Congressus Numerantium, 179 15-31 (2006) [C1]
2006Chisholm CR, MacDougall JA, 'Rational and Heron tetrahedra', Journal of Number Theory, 121 153-185 (2006) [C1]
2006Gray ID, MacDougall JA, 'Sparse semi-magic squares and vertex-magic labelings', Ars Combinatoria, 80 225-242 (2006) [C1]
2006Adams PD, Eggleton RG, MacDougall JA, 'Taxonomy of Graphs of Order 10', Congressus Numerantium, 180 65-80 (2006) [C1]
2006Miller M, Baca M, MacDougall JA, 'Vertex-magic Total Labeling of Generalized Petersen Graphs and Convex Polytopes', Journal of Combinatorial Mathematics and Combinatorial Computing, 59 89-99 (2006) [C1]

Co-authors: Mirka Miller

2005Chisholm CR, MacDougall JA, 'Rational tetrahedra with edges in arithmetic progression', Journal of Number Theory, 111 57-80 (2005) [C1]
2004Adams P, Eggleton RB, MacDougall JA, 'Structure of graph posets for orders 4 to 8', Congressus Numerantium, 166 63-81 (2004) [C1]
2004MacDougall JA, 'A generalisation of the Copair Construction for triangle-saturated graphs', Utilitas Mathematica, 66 239-247 (2004) [C1]
2004Adams P, Eggleton RB, MacDougall JA, 'Degree sequences and poset structure of order 9 graphs', Congressus Numerantuium, 166 83-95 (2004) [C1]
2003MacDougall JA, Wallis WD, 'Strong edge-magic labelling of a cycle with a chord', Australasian Journal of Combinatorics, 28 245-255 (2003) [C1]
2003MacDougall JA, 'Heron Triangles with Sides in Arithmetic Progression', Journal of Recreational Mathematics, 31 189-196 (2003) [C1]
2003Eggleton RB, MacDougall JA, 'Graph Posets, Spanning-Universal Graphs and Graph Coverings', Bulletin of the ICA, 37 63-72 (2003) [C1]
2003MacDougall JA, McSorley JP, Wallis W, Gray ID, 'Vertex-magic total labelings of trees and forests', Discrete Mathematics, 261 285-298 (2003) [C1]
2003Gray ID, MacDougall JA, Simpson RJ, Wallis WD, 'Vertex-Magic Total Labelings of Complete Bipartite Graphs', Ars Combinatoria, 69 117-127 (2003) [C1]
2003Daven M, MacDougall JA, Rodger C, 'Maximal Sets of Hamilton Cycles in Complete Multipartite Graphs', Journal of Graph Theory, 43 49-66 (2003) [C1]
2003Baca M, Bertault FA, MacDougall JA, Miller M, Simanjuntak RMG, Slamin, 'Vertex-Antimagic total labelings of graphs', Discussiones Mathematicae Graph Theory, 23 67-83 (2003) [C1]

Co-authors: Mirka Miller

2003Gray I, MacDougall JA, Wallis WD, 'On Vertex-Magic Labeling of Complete Graphs', Bulletin of the ICA, 38 42-44 (2003) [C1]
2003Adams P, Eggleton RB, MacDougall JA, Mahmoodian ES, 'Corrections to Steinbach's Posets of Graphs (Orders 5, 6, 7)', Bulletin of the ICA, 37 29-34 (2003) [C1]
2003MacDougall JA, 'Mersenne Composites and Cyclotomic Primes', Mathematical Gazette, 87 71-75 (2003) [C1]
2002MacDougall JA, Miller M, Slamin, Wallis WD, 'Vertex-Magic Total Labelings of Graphs', Utilitas Mathematica, 61 3-21 (2002) [C1]

Co-authors: Mirka Miller

2002Sweet LG, MacDougall JA, 'A decomposition theorem for homogeneous algebras', Journal of the Australian Mathematical Society, 72 47-56 (2002) [C1]
2002MacDougall JA, Miller M, Wallis WD, 'Vertex-magic total labelings of wheels and related graphs', Utilitas Mathematica, 62 175-183 (2002) [C1]

Co-authors: Mirka Miller

2002Eggleton RB, MacDougall JA, 'Minimally triangle-saturated graphs: adjoining a single vertex', Australasian Journal of Combinatorics, 25 263-278 (2002) [C1]
2001Eggleton RB, MacDougall JA, 'Minimally Star-Saturated Graphs', Congressus Numerantium, 149 161-176 (2001) [C1]
2001MacDougall JA, 'Midhat Gazale, Number: From Ahmes to Cantor', The Physicist, 38 1 (2001) [C3]
2001MacDougall JA, 'W.D. Wallis, Magic Graphs', Australian Mathematical Society Gazette, 28 275-276 (2001) [C3]
2000MacDougall JA, Buchholz RH, 'When Newton met Diophantus: A Study of Rational-Derived Polynomials and Their Extension to Quadratic Fields', Journal of Number Theory, 81 210-233 (2000) [C1]
2000Baca M, MacDougall JA, Miller M, Slamin, Wallis WD, 'Survey of Certain Valuations of Graphs', Discussiones Mathematicae Graph Theory, 20 219-229 (2000) [C1]

Co-authors: Mirka Miller

1999Buchholz RH, MacDougall JA, 'Heron Quadrilaterals with sides in arithmetic or geometric progression', Bull. Austral. Math. Soc., 59 263-269 (1999) [C1]
1999MacDougall JA, Mullen GL, 'A Note on BIB Designs with Nested Rows and Columns', Australasian Journal of Combinatorics, 20 257-259 (1999) [C1]
1999Boswell S, Eggleton RB, MacDougall JA, 'Minimally path-saturated graphs', Congressus Numerantium, 138 (1999) 97-117 (1999) [C1]
1998Eggleton RB, MacDougall JA, 'Almost $K_m$-saturated graphs', Congressus Numerantium, 131 187-203 (1998) [C1]
1988SWEET LG, MACDOUGALL JA, 'ON AUTOMORPHISMS OF ORDER-3 OF DIVISION-ALGEBRAS', LINEAR ALGEBRA AND ITS APPLICATIONS, 108 231-237 (1988)
Show 48 more

Conference (2 outputs)

YearCitationAltmetricsLink
2004MacDougall JA, Miller M, Sugeng KA, 'Super Vertex-magic Total Labellings of Graphs', Proceedings, Ballina, NSW (2004) [E1]
2004MacDougall JA, Gray ID, 'Sparse magic & anti-magic squares and magic labellings of graphs', Programme and Abstracts, Taupo, New Zealand (2004) [E3]
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Grants and Funding

Summary

Number of grants8
Total funding$34,129

- Indicates that the researcher may be seeking students for this project.

Click on a grant title below to expand the full details for that specific grant.

2008 (1 grants)

Canadian Number Theory Associaton X Meeting, Waterloo, Canada, 13/7/2008 - 18/7/2008$2,500
Funding Body: University of Newcastle

Project Team
Doctor Jim MacDougall
SchemeRole
Travel GrantChief Investigator
Total AmountFunding StartFunding Finish
$2,50020082008
GNo:G0189130

2004 (1 grants)

The 29th Australasian Conference in Combinatorial Mathematics and Combinatorial Computing, 13-18 December 2004, NZ$720
Funding Body: University of Newcastle

Project Team
Doctor Jim MacDougall
SchemeRole
Travel GrantChief Investigator
Total AmountFunding StartFunding Finish
$72020042004
GNo:G0184825

2003 (1 grants)

Magic and antimagic graph labellings.$10,000
Funding Body: University of Newcastle

Project Team
Doctor Jim MacDougall, Emeritus Professor Mirka Miller
SchemeRole
Project GrantChief Investigator
Total AmountFunding StartFunding Finish
$10,00020032003
GNo:G0182385

2002 (1 grants)

DIMACS, USA, 14-19 July 2002$2,400
Funding Body: University of Newcastle

Project Team
Doctor Jim MacDougall
SchemeRole
Travel GrantChief Investigator
Total AmountFunding StartFunding Finish
$2,40020022002
GNo:G0181939

2001 (1 grants)

Preliminary Study of the Ideal Structure of the Subgraph Lattice$5,879
Funding Body: University of Newcastle

Project Team
Doctor Jim MacDougall
SchemeRole
Early Career Researcher GrantChief Investigator
Total AmountFunding StartFunding Finish
$5,87920012001
GNo:G0181616

2000 (1 grants)

A study of graphs which are saturated with respect to star subgraphs.$2,600
Funding Body: University of Newcastle

Project Team
Doctor Jim MacDougall
SchemeRole
Early Career Researcher GrantChief Investigator
Total AmountFunding StartFunding Finish
$2,60020002000
GNo:G0179334

1999 (1 grants)

Prof Walter Wallis Visitor - 20/11/1999 to 16/12/2000.$4,880
Funding Body: University of Newcastle

Project Team
Doctor Jim MacDougall
SchemeRole
Visitor GrantChief Investigator
Total AmountFunding StartFunding Finish
$4,88019991999
GNo:G0179052

1998 (1 grants)

VISIT - MACDOUGAL - R.B. EGGLETON - ILLINOIS STATE UNI - 16/05-15/08$5,150
Funding Body: University of Newcastle

Project Team
Doctor Jim MacDougall, Professor Roger Eggleton
SchemeRole
Visitor GrantChief Investigator
Total AmountFunding StartFunding Finish
$5,15019981998
GNo:G0177642
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Research Supervision

Number of current supervisions0

For supervisions undertaken at an institution other that the University of Newcastle, the institution name is listed below the program name.

Past Supervision

YearProgramSupervisor TypeResearch Title
2007PhD (Mathematics)Sole SupervisorGraph Labelling and Decomposition
2006M Mathematics [R]Sole SupervisorNice Polynomials with Nice Derivatives
2005M Mathematics [R]Sole SupervisorRational and Heron Tetrahedra
PhD (Mathematics)Sole SupervisorConstruction Methods for Vertex-Magic Total Labelings of Graphs
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Dr James (Jim) MacDougall

Work Phone(02) 4921 6792
Fax(02) 4921 6898
Email
PositionConjoint Senior Lecturer
School of Mathematical and Physical Sciences
Faculty of Science and Information Technology
The University of Newcastle, Australia
Focus AreaMathematics
Office
V233,
Mathematics,
Callaghan
University Drive
Callaghan NSW 2308
Australia
URL:www.newcastle.edu.au/profile/jim-macdougall