Dr Jim MacDougall
Honorary Senior Lecturer
School of Information and Physical Sciences (Mathematics)
Career Summary
Biography
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
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
Professional Experience
Membership
Dates | Title | Organisation / Department |
---|---|---|
1/1/1987 - | Member - Australian Mathematical Society | Australian mathematical society Australia |
1/1/1985 - | MEMBER | Institute of Combinatorics and Its Applications Canada |
1/1/1975 - | Member - American Mathematical Society | American Mathematical Society United States |
1/1/1970 - | Member - Canadian Mathematical Society | Canadian Mathematical Society Canada |
Awards
Research Award
Year | Award |
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1983 |
Faculty Merit Award University of Prince Edward Island |
Invitations
Participant
Year | Title / Rationale |
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2002 |
2002 Connect conference Organisation: DIMACS at Rutgers Description: Invited principle speaker |
Publications
For publications that are currently unpublished or in-press, details are shown in italics.
Journal article (52 outputs)
Year | Citation | Altmetrics | Link | |||||
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2018 | Eggleton RB, Kimberley JS, MacDougall JA, 'Square-free rank of integers', Journal of Combinatorial Mathematics and Combinatorial Computing, 106 185-207 (2018) [C1] | Nova | ||||||
2012 |
MacDougall JA, Sweet LG, 'Rational homogeneous algebras', Canadian Mathematical Bulletin-Bulletin Canadien De Mathematiques, 55 351-354 (2012) [C1]
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Nova | ||||||
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]
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Nova | ||||||
2012 |
Gray ID, MacDougall JA, 'Vertex-magic labeling of regular graphs: Disjoint unions and assemblages', Discrete Applied Mathematics, 160 1114-1125 (2012) [C1]
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Nova | ||||||
2012 |
Kimberley JS, MacDougall JA, 'Mutation of vertex-magic regular graphs', Journal of Combinatorial Mathematics and Combinatorial Computing, 82 157-177 (2012) [C1]
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Nova | ||||||
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]
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Nova | ||||||
2010 |
Mohr SH, MacDougall JA, 'Integral Trees of Diameter 4', AKCE International Journal of Graphs and Combinatorics, 7 171-188 (2010) [C1]
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Nova | ||||||
2010 |
Gray ID, MacDougall JA, 'Vertex-magic labelling of non-regular graphs', Australasian Journal of Combinatorics, 46 173-183 (2010) [C1]
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Nova | ||||||
2009 |
Gray ID, MacDougall JA, 'Vertex-magic labelings of regular graphs II', Discrete Mathematics, 309 5986-5999 (2009) [C1]
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Nova | ||||||
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]
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Nova | ||||||
2009 | Adams P, Eggleton RB, MacDougall JA, 'Graphs which are linked cycles', Congressus Numerantium, 195 75-83 (2009) [C1] | Nova | ||||||
2009 | Eggleton RB, Adams P, MacDougall JA, 'Graphs which are linked structures', Congressus Numerantium, 199 75-88 (2009) [C1] | Nova | ||||||
2009 |
Gray ID, MacDougall JA, 'Vertex-magic labelings: Mutations', Australasian Journal of Combinatorics, 45 189-206 (2009) [C1]
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Nova | ||||||
2008 |
MacDougall JA, Wallis WD, 'Strong edge-magic graphs of maximum size', Discrete Mathematics, 308 2756-2763 (2008) [C1]
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Nova | ||||||
2008 |
Chisholm CR, MacDougall JA, 'Rational tetrahedra with edges in geometric progression', Journal of Number Theory, 128 251-262 (2008) [C1]
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Nova | ||||||
2008 |
Buchholz RH, MacDougall JA, 'Cyclic polygons with rational sides and area', Journal of Number Theory, 128 17-48 (2008) [C1]
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Nova | ||||||
2008 | Eggleston RB, MacDougall JA, 'Consecutive integers with equally many principal divisors', Mathematics Magazine, 81 235-248 (2008) [C1] | Nova | ||||||
2006 |
Chisholm CR, MacDougall JA, 'Rational and Heron tetrahedra', Journal of Number Theory, 121 153-185 (2006) [C1]
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Nova | ||||||
2006 |
Gray ID, MacDougall JA, 'Sparse semi-magic squares and vertex-magic labelings', Ars Combinatoria, 80 225-242 (2006) [C1]
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2006 | Adams PD, Eggleton RG, MacDougall JA, 'Graphs with a given degree sequence', Congressus Numerantium, 179 15-31 (2006) [C1] | Nova | ||||||
2006 | Adams PD, Eggleton RG, MacDougall JA, 'Taxonomy of Graphs of Order 10', Congressus Numerantium, 180 65-80 (2006) [C1] | Nova | ||||||
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] | |||||||
2006 |
Gray ID, MacDougall JA, 'Sparse anti-magic squares and vertex-magic labelings of bipartite graphs', Discrete Mathematics, 306 2878-2892 (2006) [C1]
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Nova | ||||||
2005 |
Chisholm CR, MacDougall JA, 'Rational tetrahedra with edges in arithmetic progression', Journal of Number Theory, 111 57-80 (2005) [C1]
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Nova | ||||||
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] | Nova | ||||||
2003 |
MacDougall JA, McSorley JP, Wallis W, Gray ID, 'Vertex-magic total labelings of trees and forests', Discrete Mathematics, 261 285-298 (2003) [C1]
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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]
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2003 |
Gray ID, MacDougall JA, Simpson RJ, Wallis WD, 'Vertex-Magic Total Labelings of Complete Bipartite Graphs', Ars Combinatoria, 69 117-127 (2003) [C1]
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2003 |
MacDougall JA, Wallis WD, 'Strong edge-magic labelling of a cycle with a chord', Australasian Journal of Combinatorics, 28 245-255 (2003) [C1]
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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] | |||||||
2002 |
MacDougall JA, Miller M, Wallis W, Slamin, 'Vertex-Magic Total Labelings of Graphs', Utilitas Mathematica, 61 3-21 (2002) [C1]
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2002 |
Eggleton RB, MacDougall JA, 'Minimally triangle-saturated graphs: adjoining a single vertex', Australasian Journal of Combinatorics, 25 263-278 (2002) [C1]
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Nova | ||||||
2002 |
Sweet LG, MacDougall JA, 'A decomposition theorem for homogeneous algebras', Journal of the Australian Mathematical Society, 72 47-56 (2002) [C1]
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2002 |
MacDougall JA, Miller M, Wallis WD, 'Vertex-magic total labelings of wheels and related graphs', Utilitas Mathematica, 62 175-183 (2002) [C1]
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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]
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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] | |||||||
1999 |
Buchholz RH, MacDougall JA, 'Heron Quadrilaterals with sides in arithmetic or geometric progression', Bull. Austral. Math. Soc., 59 263-269 (1999) [C1]
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Nova | ||||||
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] | |||||||
Show 49 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] |
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 |
Research Supervision
Number of supervisions
Completed4
Current0
Past Supervision
Year | Level of Study | Research Title | Program | Supervisor Type |
---|---|---|---|---|
2007 | PhD | Graph Labelling and Decomposition | PhD (Mathematics), College of Engineering, Science and Environment, The University of Newcastle | Sole Supervisor |
2006 | Masters | Nice Polynomials with Nice Derivatives | M Mathematics [R], College of Engineering, Science and Environment, The University of Newcastle | Sole Supervisor |
2005 | Masters | Rational and Heron Tetrahedra | M Mathematics [R], College of Engineering, Science and Environment, The University of Newcastle | Sole Supervisor |
2005 | PhD | Construction of Vertex-Magic Graph Labellings | Mathematics, Faculty of Science and Information Technology,The University of Newcastle | Sole Supervisor |
Dr Jim MacDougall
Position
Honorary Senior Lecturer
School of Information and Physical Sciences
College of Engineering, Science and Environment
Focus area
Mathematics
Contact Details
jim.macdougall@newcastle.edu.au |
Office
Room | V18 |
---|---|
Building | Mathematics |
Location | Callaghan University Drive Callaghan, NSW 2308 Australia |