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Dr Jim MacDougall

Conjoint Senior Lecturer

School of Mathematical and Physical Sciences (Mathematics)

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.

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)

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


Qualifications

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

Keywords

  • Graph Theory
  • Mathematics
  • Number Theory

Fields of Research

CodeDescriptionPercentage
010199Pure Mathematics not elsewhere classified80
010299Applied Mathematics not elsewhere classified5
080299Computation Theory and Mathematics not elsewhere classified15

Professional Experience

UON Appointment

DatesTitleOrganisation / Department
1/01/2008 - 28/01/2011Senior LecturerUniversity of Newcastle
School of Mathematical and Physical Sciences
Australia

Membership

DatesTitleOrganisation / Department
Member - American Mathematical SocietyAmerican Mathematical Society
United States
Member - Canadian Mathematical SocietyCanadian Mathematical Society
Canada
Member - Australian Mathematical SocietyAustralian mathematical society
Australia

Awards

Research Award

YearAward
1983Faculty Merit Award
Unknown

Invitations

Participant

YearTitle / Rationale
20022002 Connect conference
Organisation: DIMACS at Rutgers Description: Invited principle speaker
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Publications

For publications that are currently unpublished or in-press, details are shown in italics.


Journal article (51 outputs)

YearCitationAltmetricsLink
2012MacDougall JA, Sweet LG, 'Rational homogeneous algebras', Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques, 55 351-354 (2012) [C1]
DOI10.4153/CMB-2011-087-5
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]
CitationsScopus - 2Web of Science - 2
2012Gray ID, MacDougall JA, 'Vertex-magic labeling of regular graphs: Disjoint unions and assemblages', Discrete Applied Mathematics, 160 1114-1125 (2012) [C1]
DOI10.1016/j.dam.2011.11.025
2012Kimberley JS, MacDougall JA, 'Mutation of vertex-magic regular graphs', Journal of Combinatorial Mathematics and Combinatorial Computing, 82 157-177 (2012) [C1]
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]
2011Kimberley JS, MacDougall JA, 'All regular graphs of small odd order are vertex-magic', Australasian Journal of Combinatorics, 51 175-199 (2011) [C1]
CitationsScopus - 1
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]
CitationsScopus - 2
2009Gray ID, MacDougall JA, 'Vertex-magic labelings of regular graphs II', Discrete Mathematics, 309 5986-5999 (2009) [C1]
DOI10.1016/j.disc.2009.04.031
CitationsScopus - 15Web of Science - 5
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]
DOI10.1016/j.laa.2009.03.048
CitationsScopus - 2
2009Adams P, Eggleton RB, MacDougall JA, 'Graphs which are linked cycles', Congressus Numerantium, 195 75-83 (2009) [C1]
2009Eggleton RB, Adams P, MacDougall JA, 'Graphs which are linked structures', Congressus Numerantium, 199 75-88 (2009) [C1]
2009Gray ID, MacDougall JA, 'Vertex-magic labelings: Mutations', Australasian Journal of Combinatorics, 45 189-206 (2009) [C1]
CitationsScopus - 3
2008MacDougall JA, Wallis WD, 'Strong edge-magic graphs of maximum size', Discrete Mathematics, 308 2756-2763 (2008) [C1]
DOI10.1016/j.disc.2006.12.009
CitationsScopus - 2
2008Chisholm CR, MacDougall JA, 'Rational tetrahedra with edges in geometric progression', Journal of Number Theory, 128 251-262 (2008) [C1]
DOI10.1016/j.jnt.2007.07.002
2008Buchholz RH, MacDougall JA, 'Cyclic polygons with rational sides and area', Journal of Number Theory, 128 17-48 (2008) [C1]
DOI10.1016/j.jnt.2007.05.005
2008Eggleston RB, MacDougall JA, 'Consecutive integers with equally many principal divisors', Mathematics Magazine, 81 235-248 (2008) [C1]
2006Chisholm CR, MacDougall JA, 'Rational and Heron tetrahedra', Journal of Number Theory, 121 153-185 (2006) [C1]
DOI10.1016/j.jnt.2006.02.009
CitationsScopus - 1Web of Science - 1
2006Gray ID, MacDougall JA, 'Sparse semi-magic squares and vertex-magic labelings', Ars Combinatoria, 80 225-242 (2006) [C1]
CitationsScopus - 5Web of Science - 2
2006Adams PD, Eggleton RG, MacDougall JA, 'Graphs with a given degree sequence', Congressus Numerantium, 179 15-31 (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-authorsMirka Miller
2006Gray ID, MacDougall JA, 'Sparse anti-magic squares and vertex-magic labelings of bipartite graphs', Discrete Mathematics, 306 2878-2892 (2006) [C1]
DOI10.1016/j.disc.2006.04.032
CitationsScopus - 3
2005Chisholm CR, MacDougall JA, 'Rational tetrahedra with edges in arithmetic progression', Journal of Number Theory, 111 57-80 (2005) [C1]
DOI10.1016/j.jnt.2004.07.009
CitationsScopus - 1Web of Science - 1
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, 'Structure of graph posets for orders 4 to 8', Congressus Numerantium, 166 63-81 (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, McSorley JP, Wallis W, Gray ID, 'Vertex-magic total labelings of trees and forests', Discrete Mathematics, 261 285-298 (2003) [C1]
DOI10.1016/S0012-365X(02)00475-2
CitationsWeb of Science - 8
2003MacDougall JA, 'Heron Triangles with Sides in Arithmetic Progression', Journal of Recreational Mathematics, 31 189-196 (2003) [C1]
2003MacDougall JA, 'Mersenne Composites and Cyclotomic Primes', Mathematical Gazette, 87 71-75 (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]
DOI10.1002/jgt.10096
CitationsScopus - 4Web of Science - 2
2003Gray ID, MacDougall JA, Simpson RJ, Wallis WD, 'Vertex-Magic Total Labelings of Complete Bipartite Graphs', Ars Combinatoria, 69 117-127 (2003) [C1]
CitationsScopus - 13Web of Science - 7
2003MacDougall JA, Wallis WD, 'Strong edge-magic labelling of a cycle with a chord', Australasian Journal of Combinatorics, 28 245-255 (2003) [C1]
CitationsScopus - 11
2003Eggleton RB, MacDougall JA, 'Graph Posets, Spanning-Universal Graphs and Graph Coverings', Bulletin of the ICA, 37 63-72 (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]
2003Gray I, MacDougall JA, Wallis WD, 'On Vertex-Magic Labeling of Complete Graphs', Bulletin of the ICA, 38 42-44 (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-authorsMirka Miller
2002MacDougall JA, Miller M, Wallis W, Slamin, 'Vertex-Magic Total Labelings of Graphs', Utilitas Mathematica, 61 3-21 (2002) [C1]
CitationsScopus - 66Web of Science - 31
Co-authorsMirka Miller
2002Eggleton RB, MacDougall JA, 'Minimally triangle-saturated graphs: adjoining a single vertex', Australasian Journal of Combinatorics, 25 263-278 (2002) [C1]
CitationsScopus - 1
2002Sweet LG, MacDougall JA, 'A decomposition theorem for homogeneous algebras', Journal of the Australian Mathematical Society, 72 47-56 (2002) [C1]
CitationsScopus - 2Web of Science - 2
2002MacDougall JA, Miller M, Wallis WD, 'Vertex-magic total labelings of wheels and related graphs', Utilitas Mathematica, 62 175-183 (2002) [C1]
CitationsScopus - 17Web of Science - 5
Co-authorsMirka Miller
2001MacDougall JA, 'W.D. Wallis, Magic Graphs', Australian Mathematical Society Gazette, 28 275-276 (2001) [C3]
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]
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]
CitationsScopus - 3Web of Science - 3
2000Baca M, MacDougall JA, Miller M, Wallis WD, Slamin, 'Survey of certain valuations of graphs', Discussiones Mathematicae: Graph Theory, 20 219-229 (2000) [C1]
Co-authorsMirka Miller
1999Buchholz RH, MacDougall JA, 'Heron Quadrilaterals with sides in arithmetic or geometric progression', Bull. Austral. Math. Soc., 59 263-269 (1999) [C1]
DOI10.1017/S0004972700032883
CitationsScopus - 6Web of Science - 5
1999Boswell S, Eggleton RB, MacDougall JA, 'Minimally path-saturated graphs', Congressus Numerantium, 138 (1999) 97-117 (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]
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)
DOI10.1016/0024-3795(88)90190-5Author URL
Show 48 more journal articles

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

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


20081 grants / $2,500

Canadian Number Theory Associaton X Meeting, Waterloo, Canada, 13/7/2008 - 18/7/2008$2,500

Funding body: University of Newcastle

Funding bodyUniversity of Newcastle
Project TeamDoctor Jim MacDougall
SchemeTravel Grant
RoleLead
Funding Start2008
Funding Finish2008
GNoG0189130
Type Of FundingInternal
CategoryINTE
UONY

20041 grants / $720

The 29th Australasian Conference in Combinatorial Mathematics and Combinatorial Computing, 13-18 December 2004, NZ$720

Funding body: University of Newcastle

Funding bodyUniversity of Newcastle
Project TeamDoctor Jim MacDougall
SchemeTravel Grant
RoleLead
Funding Start2004
Funding Finish2004
GNoG0184825
Type Of FundingInternal
CategoryINTE
UONY

20031 grants / $10,000

Magic and antimagic graph labellings.$10,000

Funding body: University of Newcastle

Funding bodyUniversity of Newcastle
Project TeamDoctor Jim MacDougall, Emeritus Professor Mirka Miller
SchemeProject Grant
RoleLead
Funding Start2003
Funding Finish2003
GNoG0182385
Type Of FundingInternal
CategoryINTE
UONY

20021 grants / $2,400

DIMACS, USA, 14-19 July 2002$2,400

Funding body: University of Newcastle

Funding bodyUniversity of Newcastle
Project TeamDoctor Jim MacDougall
SchemeTravel Grant
RoleLead
Funding Start2002
Funding Finish2002
GNoG0181939
Type Of FundingInternal
CategoryINTE
UONY

20011 grants / $5,879

Preliminary Study of the Ideal Structure of the Subgraph Lattice$5,879

Funding body: University of Newcastle

Funding bodyUniversity of Newcastle
Project TeamDoctor Jim MacDougall
SchemeEarly Career Researcher Grant
RoleLead
Funding Start2001
Funding Finish2001
GNoG0181616
Type Of FundingInternal
CategoryINTE
UONY

20001 grants / $2,600

A study of graphs which are saturated with respect to star subgraphs.$2,600

Funding body: University of Newcastle

Funding bodyUniversity of Newcastle
Project TeamDoctor Jim MacDougall
SchemeEarly Career Researcher Grant
RoleLead
Funding Start2000
Funding Finish2000
GNoG0179334
Type Of FundingInternal
CategoryINTE
UONY

19991 grants / $4,880

Prof Walter Wallis Visitor - 20/11/1999 to 16/12/2000.$4,880

Funding body: University of Newcastle

Funding bodyUniversity of Newcastle
Project TeamDoctor Jim MacDougall
SchemeVisitor Grant
RoleLead
Funding Start1999
Funding Finish1999
GNoG0179052
Type Of FundingInternal
CategoryINTE
UONY

19981 grants / $5,150

VISIT - MACDOUGAL - R.B. EGGLETON - ILLINOIS STATE UNI - 16/05-15/08$5,150

Funding body: University of Newcastle

Funding bodyUniversity of Newcastle
Project TeamDoctor Jim MacDougall, Professor Roger Eggleton
SchemeVisitor Grant
RoleLead
Funding Start1998
Funding Finish1998
GNoG0177642
Type Of FundingInternal
CategoryINTE
UONY
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Research Supervision

Past Supervision

YearResearch Title / Program / Supervisor Type
2007Graph Labelling and Decomposition
Mathematics, Faculty of Science and Information Technology
Sole Supervisor
2006Nice Polynomials with Nice Derivatives
Mathematics, Faculty of Science and Information Technology
Sole Supervisor
2005Rational and Heron Tetrahedra
Mathematics, Faculty of Science and Information Technology
Sole Supervisor
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Dr Jim MacDougall

Position

Conjoint Senior Lecturer
School of Mathematical and Physical Sciences
Faculty of Science and Information Technology

Focus area

Mathematics

Contact Details

Emailjim.macdougall@newcastle.edu.au
Phone(02) 4921 6792
Fax(02) 4921 6898

Office

RoomV233
BuildingMathematics
LocationCallaghan
University Drive
Callaghan, NSW 2308
Australia
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