Dr Jim MacDougall
Conjoint Senior Lecturer
School of Mathematical 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 antimagic labelings. Related combinatorial arrays such as sparse magic and antimagic 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 rationalsided 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. anticommutative algebras, nilpotent algebras or quasidivision 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 antimagic labelings. Related combinatorial arrays such as sparse magic and antimagic 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 rationalsided 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. anticommutative algebras, nilpotent algebras or quasidivision 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 

1/1/1970   Member  Canadian Mathematical Society  Canadian Mathematical Society Canada 
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 
Awards
Research Award
Year  Award 

1983 
Faculty Merit Award University of Prince Edward Island 
Invitations
Participant
Year  Title / Rationale 

2002 
2002 Connect conference Organisation: DIMACS at Rutgers Description: Invited principle speaker 
Publications
For publications that are currently unpublished or inpress, details are shown in italics.
Journal article (52 outputs)
Year  Citation  Altmetrics  Link  

2018  Eggleton RB, Kimberley JS, MacDougall JA, 'Squarefree rank of integers', Journal of Combinatorial Mathematics and Combinatorial Computing, 106 185207 (2018) [C1]  
2012 
MacDougall JA, Sweet LG, 'Rational homogeneous algebras', Canadian Mathematical BulletinBulletin Canadien De Mathematiques, 55 351354 (2012) [C1]


2012 
MacDonald GW, MacDougall JA, Sweet LG, 'On the dimension of linear spaces of nilpotent matrices', Linear Algebra and Its Applications, 436 22102230 (2012) [C1]


2012 
Gray ID, MacDougall JA, 'Vertexmagic labeling of regular graphs: Disjoint unions and assemblages', Discrete Applied Mathematics, 160 11141125 (2012) [C1]


2012 
Kimberley JS, MacDougall JA, 'Mutation of vertexmagic regular graphs', Journal of Combinatorial Mathematics and Combinatorial Computing, 82 157177 (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 3038 (2012) [C1]  
2011 
Kimberley JS, MacDougall JA, 'All regular graphs of small odd order are vertexmagic', Australasian Journal of Combinatorics, 51 175199 (2011) [C1]


2010 
Mohr SH, MacDougall JA, 'Integral Trees of Diameter 4', AKCE International Journal of Graphs and Combinatorics, 7 171188 (2010) [C1]


2010 
Gray ID, MacDougall JA, 'Vertexmagic labelling of nonregular graphs', Australasian Journal of Combinatorics, 46 173183 (2010) [C1]


2009 
Gray ID, MacDougall JA, 'Vertexmagic labelings of regular graphs II', Discrete Mathematics, 309 59865999 (2009) [C1]


2009 
Sweet LG, MacDougall JA, 'The maximum dimension of a subspace of nilpotent matrices of index 2', Linear Algebra and Its Applications, 431 11161124 (2009) [C1]


2009  Adams P, Eggleton RB, MacDougall JA, 'Graphs which are linked cycles', Congressus Numerantium, 195 7583 (2009) [C1]  
2009  Eggleton RB, Adams P, MacDougall JA, 'Graphs which are linked structures', Congressus Numerantium, 199 7588 (2009) [C1]  
2009 
Gray ID, MacDougall JA, 'Vertexmagic labelings: Mutations', Australasian Journal of Combinatorics, 45 189206 (2009) [C1]


2008 
MacDougall JA, Wallis WD, 'Strong edgemagic graphs of maximum size', Discrete Mathematics, 308 27562763 (2008) [C1]


2008 
Chisholm CR, MacDougall JA, 'Rational tetrahedra with edges in geometric progression', Journal of Number Theory, 128 251262 (2008) [C1]


2008 
Buchholz RH, MacDougall JA, 'Cyclic polygons with rational sides and area', Journal of Number Theory, 128 1748 (2008) [C1]


2008  Eggleston RB, MacDougall JA, 'Consecutive integers with equally many principal divisors', Mathematics Magazine, 81 235248 (2008) [C1]  
2006 
Chisholm CR, MacDougall JA, 'Rational and Heron tetrahedra', Journal of Number Theory, 121 153185 (2006) [C1]


2006 
Gray ID, MacDougall JA, 'Sparse semimagic squares and vertexmagic labelings', Ars Combinatoria, 80 225242 (2006) [C1]


2006  Adams PD, Eggleton RG, MacDougall JA, 'Graphs with a given degree sequence', Congressus Numerantium, 179 1531 (2006) [C1]  
2006  Adams PD, Eggleton RG, MacDougall JA, 'Taxonomy of Graphs of Order 10', Congressus Numerantium, 180 6580 (2006) [C1]  
2006  Miller M, Baca M, MacDougall JA, 'Vertexmagic Total Labeling of Generalized Petersen Graphs and Convex Polytopes', Journal of Combinatorial Mathematics and Combinatorial Computing, 59 8999 (2006) [C1]  
2006 
Gray ID, MacDougall JA, 'Sparse antimagic squares and vertexmagic labelings of bipartite graphs', Discrete Mathematics, 306 28782892 (2006) [C1]


2005 
Chisholm CR, MacDougall JA, 'Rational tetrahedra with edges in arithmetic progression', Journal of Number Theory, 111 5780 (2005) [C1]


2004  MacDougall JA, 'A generalisation of the Copair Construction for trianglesaturated graphs', Utilitas Mathematica, 66 239247 (2004) [C1]  
2004  Adams P, Eggleton RB, MacDougall JA, 'Structure of graph posets for orders 4 to 8', Congressus Numerantium, 166 6381 (2004) [C1]  
2004  Adams P, Eggleton RB, MacDougall JA, 'Degree sequences and poset structure of order 9 graphs', Congressus Numerantuium, 166 8395 (2004) [C1]  
2003 
MacDougall JA, McSorley JP, Wallis W, Gray ID, 'Vertexmagic total labelings of trees and forests', Discrete Mathematics, 261 285298 (2003) [C1]


2003  MacDougall JA, 'Heron Triangles with Sides in Arithmetic Progression', Journal of Recreational Mathematics, 31 189196 (2003) [C1]  
2003  MacDougall JA, 'Mersenne Composites and Cyclotomic Primes', Mathematical Gazette, 87 7175 (2003) [C1]  
2003 
Daven M, MacDougall JA, Rodger C, 'Maximal Sets of Hamilton Cycles in Complete Multipartite Graphs', Journal of Graph Theory, 43 4966 (2003) [C1]


2003 
Gray ID, MacDougall JA, Simpson RJ, Wallis WD, 'VertexMagic Total Labelings of Complete Bipartite Graphs', Ars Combinatoria, 69 117127 (2003) [C1]


2003 
MacDougall JA, Wallis WD, 'Strong edgemagic labelling of a cycle with a chord', Australasian Journal of Combinatorics, 28 245255 (2003) [C1]


2003  Eggleton RB, MacDougall JA, 'Graph Posets, SpanningUniversal Graphs and Graph Coverings', Bulletin of the ICA, 37 6372 (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 2934 (2003) [C1]  
2003  Gray I, MacDougall JA, Wallis WD, 'On VertexMagic Labeling of Complete Graphs', Bulletin of the ICA, 38 4244 (2003) [C1]  
2003  Baca M, Bertault FA, MacDougall JA, Miller M, Simanjuntak RMG, Slamin, 'VertexAntimagic total labelings of graphs', Discussiones Mathematicae Graph Theory, 23 6783 (2003) [C1]  
2002 
MacDougall JA, Miller M, Wallis W, Slamin, 'VertexMagic Total Labelings of Graphs', Utilitas Mathematica, 61 321 (2002) [C1]


2002 
Eggleton RB, MacDougall JA, 'Minimally trianglesaturated graphs: adjoining a single vertex', Australasian Journal of Combinatorics, 25 263278 (2002) [C1]


2002 
Sweet LG, MacDougall JA, 'A decomposition theorem for homogeneous algebras', Journal of the Australian Mathematical Society, 72 4756 (2002) [C1]


2002 
MacDougall JA, Miller M, Wallis WD, 'Vertexmagic total labelings of wheels and related graphs', Utilitas Mathematica, 62 175183 (2002) [C1]


2001  MacDougall JA, 'W.D. Wallis, Magic Graphs', Australian Mathematical Society Gazette, 28 275276 (2001) [C3]  
2001  Eggleton RB, MacDougall JA, 'Minimally StarSaturated Graphs', Congressus Numerantium, 149 161176 (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 RationalDerived Polynomials and Their Extension to Quadratic Fields', Journal of Number Theory, 81 210233 (2000) [C1]


2000  Baca M, MacDougall JA, Miller M, Wallis WD, Slamin, 'Survey of certain valuations of graphs', Discussiones Mathematicae: Graph Theory, 20 219229 (2000) [C1]  
1999 
Buchholz RH, MacDougall JA, 'Heron Quadrilaterals with sides in arithmetic or geometric progression', Bull. Austral. Math. Soc., 59 263269 (1999) [C1]


1999  Boswell S, Eggleton RB, MacDougall JA, 'Minimally pathsaturated graphs', Congressus Numerantium, 138 (1999) 97117 (1999) [C1]  
1999  MacDougall JA, Mullen GL, 'A Note on BIB Designs with Nested Rows and Columns', Australasian Journal of Combinatorics, 20 257259 (1999) [C1]  
1998  Eggleton RB, MacDougall JA, 'Almost $K_m$saturated graphs', Congressus Numerantium, 131 187203 (1998) [C1]  
Show 49 more journal articles 
Conference (2 outputs)
Year  Citation  Altmetrics  Link 

2004  MacDougall JA, Miller M, Sugeng KA, 'Super Vertexmagic Total Labellings of Graphs', Proceedings, Ballina, NSW (2004) [E1]  
2004  MacDougall JA, Gray ID, 'Sparse magic & antimagic 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, 1318 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, 1419 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  16/0515/08$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 VertexMagic Graph Labellings  Mathematics, Faculty of Science and Information Technology,The University of Newcastle  Sole Supervisor 
Dr Jim MacDougall
Position
Conjoint Senior Lecturer
School of Mathematical and Physical Sciences
College of Engineering, Science and Environment
Focus area
Mathematics
Contact Details
jim.macdougall@newcastle.edu.au 
Office
Room  V.18 

Building  Mathematics 
Location  Callaghan University Drive Callaghan, NSW 2308 Australia 