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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

Code Description Percentage
010199 Pure Mathematics not elsewhere classified 80
010299 Applied Mathematics not elsewhere classified 5
080299 Computation Theory and Mathematics not elsewhere classified 15

Professional Experience

UON Appointment

Title Organisation / Department

Membership

Dates Title Organisation / Department
Member - American Mathematical Society American Mathematical Society
United States
Member - Canadian Mathematical Society Canadian Mathematical Society
Canada
Member - Australian Mathematical Society Australian mathematical society
Australia

Awards

Research Award

Year Award
1983 Faculty Merit Award
Unknown

Invitations

Participant

Year Title / Rationale
2002 2002 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)

Year Citation Altmetrics Link
2012 MacDougall JA, Sweet LG, 'Rational homogeneous algebras', Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques, 55 351-354 (2012) [C1]
DOI 10.4153/CMB-2011-087-5
2012 MacDonald GW, MacDougall JA, Sweet LG, 'On the dimension of linear spaces of nilpotent matrices', Linear Algebra and Its Applications, 436 2210-2230 (2012) [C1]
Citations Scopus - 2Web of Science - 2
2012 Gray ID, MacDougall JA, 'Vertex-magic labeling of regular graphs: Disjoint unions and assemblages', Discrete Applied Mathematics, 160 1114-1125 (2012) [C1]
DOI 10.1016/j.dam.2011.11.025
2012 Kimberley JS, MacDougall JA, 'Mutation of vertex-magic regular graphs', Journal of Combinatorial Mathematics and Combinatorial Computing, 82 157-177 (2012) [C1]
2012 Eggleton 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]
2011 Kimberley JS, MacDougall JA, 'All regular graphs of small odd order are vertex-magic', Australasian Journal of Combinatorics, 51 175-199 (2011) [C1]
Citations Scopus - 1
2010 Mohr SH, MacDougall JA, 'Integral Trees of Diameter 4', AKCE International Journal of Graphs and Combinatorics, 7 171-188 (2010) [C1]
2010 Gray ID, MacDougall JA, 'Vertex-magic labelling of non-regular graphs', Australasian Journal of Combinatorics, 46 173-183 (2010) [C1]
Citations Scopus - 2
2009 Gray ID, MacDougall JA, 'Vertex-magic labelings of regular graphs II', Discrete Mathematics, 309 5986-5999 (2009) [C1]
DOI 10.1016/j.disc.2009.04.031
Citations Scopus - 15Web of Science - 5
2009 Sweet 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]
DOI 10.1016/j.laa.2009.03.048
Citations Scopus - 2
2009 Adams P, Eggleton RB, MacDougall JA, 'Graphs which are linked cycles', Congressus Numerantium, 195 75-83 (2009) [C1]
2009 Eggleton RB, Adams P, MacDougall JA, 'Graphs which are linked structures', Congressus Numerantium, 199 75-88 (2009) [C1]
2009 Gray ID, MacDougall JA, 'Vertex-magic labelings: Mutations', Australasian Journal of Combinatorics, 45 189-206 (2009) [C1]
Citations Scopus - 3
2008 MacDougall JA, Wallis WD, 'Strong edge-magic graphs of maximum size', Discrete Mathematics, 308 2756-2763 (2008) [C1]
DOI 10.1016/j.disc.2006.12.009
Citations Scopus - 2
2008 Chisholm CR, MacDougall JA, 'Rational tetrahedra with edges in geometric progression', Journal of Number Theory, 128 251-262 (2008) [C1]
DOI 10.1016/j.jnt.2007.07.002
2008 Buchholz RH, MacDougall JA, 'Cyclic polygons with rational sides and area', Journal of Number Theory, 128 17-48 (2008) [C1]
DOI 10.1016/j.jnt.2007.05.005
2008 Eggleston RB, MacDougall JA, 'Consecutive integers with equally many principal divisors', Mathematics Magazine, 81 235-248 (2008) [C1]
2006 Chisholm CR, MacDougall JA, 'Rational and Heron tetrahedra', Journal of Number Theory, 121 153-185 (2006) [C1]
DOI 10.1016/j.jnt.2006.02.009
Citations Scopus - 1Web of Science - 1
2006 Gray ID, MacDougall JA, 'Sparse semi-magic squares and vertex-magic labelings', Ars Combinatoria, 80 225-242 (2006) [C1]
Citations Scopus - 5Web of Science - 2
2006 Adams PD, Eggleton RG, MacDougall JA, 'Graphs with a given degree sequence', Congressus Numerantium, 179 15-31 (2006) [C1]
2006 Adams PD, Eggleton RG, MacDougall JA, 'Taxonomy of Graphs of Order 10', Congressus Numerantium, 180 65-80 (2006) [C1]
2006 Miller 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
2006 Gray ID, MacDougall JA, 'Sparse anti-magic squares and vertex-magic labelings of bipartite graphs', Discrete Mathematics, 306 2878-2892 (2006) [C1]
DOI 10.1016/j.disc.2006.04.032
Citations Scopus - 3
2005 Chisholm CR, MacDougall JA, 'Rational tetrahedra with edges in arithmetic progression', Journal of Number Theory, 111 57-80 (2005) [C1]
DOI 10.1016/j.jnt.2004.07.009
Citations Scopus - 1Web of Science - 1
2004 MacDougall JA, 'A generalisation of the Copair Construction for triangle-saturated graphs', Utilitas Mathematica, 66 239-247 (2004) [C1]
2004 Adams P, Eggleton RB, MacDougall JA, 'Structure of graph posets for orders 4 to 8', Congressus Numerantium, 166 63-81 (2004) [C1]
2004 Adams P, Eggleton RB, MacDougall JA, 'Degree sequences and poset structure of order 9 graphs', Congressus Numerantuium, 166 83-95 (2004) [C1]
2003 MacDougall JA, McSorley JP, Wallis W, Gray ID, 'Vertex-magic total labelings of trees and forests', Discrete Mathematics, 261 285-298 (2003) [C1]
DOI 10.1016/S0012-365X(02)00475-2
Citations Web of Science - 8
2003 MacDougall JA, 'Heron Triangles with Sides in Arithmetic Progression', Journal of Recreational Mathematics, 31 189-196 (2003) [C1]
2003 MacDougall JA, 'Mersenne Composites and Cyclotomic Primes', Mathematical Gazette, 87 71-75 (2003) [C1]
2003 Daven M, MacDougall JA, Rodger C, 'Maximal Sets of Hamilton Cycles in Complete Multipartite Graphs', Journal of Graph Theory, 43 49-66 (2003) [C1]
DOI 10.1002/jgt.10096
Citations Scopus - 4Web of Science - 2
2003 Gray ID, MacDougall JA, Simpson RJ, Wallis WD, 'Vertex-Magic Total Labelings of Complete Bipartite Graphs', Ars Combinatoria, 69 117-127 (2003) [C1]
Citations Scopus - 13Web of Science - 7
2003 MacDougall JA, Wallis WD, 'Strong edge-magic labelling of a cycle with a chord', Australasian Journal of Combinatorics, 28 245-255 (2003) [C1]
Citations Scopus - 11
2003 Eggleton RB, MacDougall JA, 'Graph Posets, Spanning-Universal Graphs and Graph Coverings', Bulletin of the ICA, 37 63-72 (2003) [C1]
2003 Adams 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]
2003 Gray I, MacDougall JA, Wallis WD, 'On Vertex-Magic Labeling of Complete Graphs', Bulletin of the ICA, 38 42-44 (2003) [C1]
2003 Baca 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
2002 MacDougall JA, Miller M, Wallis W, Slamin, 'Vertex-Magic Total Labelings of Graphs', Utilitas Mathematica, 61 3-21 (2002) [C1]
Citations Scopus - 67Web of Science - 31
Co-authors Mirka Miller
2002 Eggleton RB, MacDougall JA, 'Minimally triangle-saturated graphs: adjoining a single vertex', Australasian Journal of Combinatorics, 25 263-278 (2002) [C1]
Citations Scopus - 1
2002 Sweet LG, MacDougall JA, 'A decomposition theorem for homogeneous algebras', Journal of the Australian Mathematical Society, 72 47-56 (2002) [C1]
Citations Scopus - 2Web of Science - 2
2002 MacDougall JA, Miller M, Wallis WD, 'Vertex-magic total labelings of wheels and related graphs', Utilitas Mathematica, 62 175-183 (2002) [C1]
Citations Scopus - 17Web of Science - 5
Co-authors Mirka Miller
2001 MacDougall JA, 'W.D. Wallis, Magic Graphs', Australian Mathematical Society Gazette, 28 275-276 (2001) [C3]
2001 Eggleton RB, MacDougall JA, 'Minimally Star-Saturated Graphs', Congressus Numerantium, 149 161-176 (2001) [C1]
2001 MacDougall JA, 'Midhat Gazale, Number: From Ahmes to Cantor', The Physicist, 38 1 (2001) [C3]
2000 MacDougall 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]
Citations Scopus - 3Web of Science - 3
2000 Baca M, MacDougall JA, Miller M, Wallis WD, Slamin, 'Survey of certain valuations of graphs', Discussiones Mathematicae: Graph Theory, 20 219-229 (2000) [C1]
Co-authors Mirka Miller
1999 Buchholz RH, MacDougall JA, 'Heron Quadrilaterals with sides in arithmetic or geometric progression', Bull. Austral. Math. Soc., 59 263-269 (1999) [C1]
DOI 10.1017/S0004972700032883
Citations Scopus - 6Web of Science - 5
1999 Boswell S, Eggleton RB, MacDougall JA, 'Minimally path-saturated graphs', Congressus Numerantium, 138 (1999) 97-117 (1999) [C1]
1999 MacDougall JA, Mullen GL, 'A Note on BIB Designs with Nested Rows and Columns', Australasian Journal of Combinatorics, 20 257-259 (1999) [C1]
1998 Eggleton RB, MacDougall JA, 'Almost $K_m$-saturated graphs', Congressus Numerantium, 131 187-203 (1998) [C1]
1988 SWEET LG, MACDOUGALL JA, 'ON AUTOMORPHISMS OF ORDER-3 OF DIVISION-ALGEBRAS', LINEAR ALGEBRA AND ITS APPLICATIONS, 108 231-237 (1988)
DOI 10.1016/0024-3795(88)90190-5
Show 48 more journal articles

Conference (2 outputs)

Year Citation Altmetrics Link
2004 MacDougall JA, Miller M, Sugeng KA, 'Super Vertex-magic Total Labellings of Graphs', Proceedings, Ballina, NSW (2004) [E1]
2004 MacDougall 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 grants 8
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 body University of Newcastle
Project Team Doctor Jim MacDougall
Scheme Travel Grant
Role Lead
Funding Start 2008
Funding Finish 2008
GNo G0189130
Type Of Funding Internal
Category INTE
UON Y

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 body University of Newcastle
Project Team Doctor Jim MacDougall
Scheme Travel Grant
Role Lead
Funding Start 2004
Funding Finish 2004
GNo G0184825
Type Of Funding Internal
Category INTE
UON Y

20031 grants / $10,000

Magic and antimagic graph labellings.$10,000

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Doctor Jim MacDougall, Emeritus Professor Mirka Miller
Scheme Project Grant
Role Lead
Funding Start 2003
Funding Finish 2003
GNo G0182385
Type Of Funding Internal
Category INTE
UON Y

20021 grants / $2,400

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

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Doctor Jim MacDougall
Scheme Travel Grant
Role Lead
Funding Start 2002
Funding Finish 2002
GNo G0181939
Type Of Funding Internal
Category INTE
UON Y

20011 grants / $5,879

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

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Doctor Jim MacDougall
Scheme Early Career Researcher Grant
Role Lead
Funding Start 2001
Funding Finish 2001
GNo G0181616
Type Of Funding Internal
Category INTE
UON Y

20001 grants / $2,600

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

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Doctor Jim MacDougall
Scheme Early Career Researcher Grant
Role Lead
Funding Start 2000
Funding Finish 2000
GNo G0179334
Type Of Funding Internal
Category INTE
UON Y

19991 grants / $4,880

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

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Doctor Jim MacDougall
Scheme Visitor Grant
Role Lead
Funding Start 1999
Funding Finish 1999
GNo G0179052
Type Of Funding Internal
Category INTE
UON Y

19981 grants / $5,150

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

Funding body: University of Newcastle

Funding body University of Newcastle
Project Team Doctor Jim MacDougall, Professor Roger Eggleton
Scheme Visitor Grant
Role Lead
Funding Start 1998
Funding Finish 1998
GNo G0177642
Type Of Funding Internal
Category INTE
UON Y
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Research Supervision

Past Supervision

Year Research Title / Program / Supervisor Type
2007 Graph Labelling and Decomposition
Mathematics, Faculty of Science and Information Technology
Sole Supervisor
2006 Nice Polynomials with Nice Derivatives
Mathematics, Faculty of Science and Information Technology
Sole Supervisor
2005 Rational 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

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

Office

Room V233
Building Mathematics
Location Callaghan
University Drive
Callaghan, NSW 2308
Australia
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