Research
Interests
- Formal Methods in Software
Development and Model Checking
- Electronic Voting Systems
- Graph Theory and Graph
Algorithms, Applications to Bioinformatics and Bayesian Networks
- Educational Software on Mobile Platforms
Publications
- "Software Systems for Research in Graph Theory, "The Journal
of Combinatorial Mathematics and Combinatorial Computing, vol. LXIX, May 2009, pp 53-62.
(with A. Heinz).
- "Degree Sets in Polygon Visibility Graphs,"
The Journal of Combinatorial Mathematics and Combinatorial Computing, vol. LXIX, May 2009, pp 63-74.
(with John Emert, J. Michael McGrew, and Frank W. Owens).
- "The Biocomputational Immersive Learning,"
Ball State University Undergraduate Mathematics Exchange, Vol. 5, No. 1, (Spring 2008).
(with A. Blakey and M. Begum).
- "An Algorithm for Graceful Labelings of Cycles,"
Congressus Numerantium, 186 (2007), pp. 57-63.
(with Adrian Heinz and Mahbubul Majumder).
- "Properties of Graceful Labelings of Cycles,"
Congressus Numerantium, 188 (2007), pp. 109-115.
(with Adrian Heinz and Mahbubul Majumder).
- "Software Systems for Implementing Graph Algorithms for Learning and Research , ICTACS 2006, Proceedings of the First International Conference on Theories and Applications of Computer Science 2006, World Scientific
Publishers. (with Adrian Heinz).
- "On Avoiding a Clash of Arms
at a Round Table," Congressus Numerantium,
179 (2006), pp. 215-219. (with John Emert, J. Michael McGrew,
and Frank W. Owens).
- "The structure of super line
graphs," Proceedings, 8th International Symposium on Parallel
Architectures, Algorithms & Networks (I-SPAN 2005), pp 468-471. IEEE
Computer Society. (with R. Ellis and D. Ferrero).
- "Old and New Generalizations
of Line Graphs," International Journal of Mathematics and Mathematical
Sciences 2004: 29, 1509-1521.
- "Connectivity Properties
of Visibility Graphs,"Congressus
Numerantium, 165 (2003), pp.
189-194. ( with John Emert and M. McGrew).
- "A Cluster-Oriented Mutual
Exclusion Algorithm for Mobile Ad-hoc Networks," Proceedings of the
International Conference on Parallel and Distributed Processing Techniques
and Applications, Volume II, CSREA Press, 2003. (with S.
Udgata)
- ``JGraph - A Java Based
System for Drawing Graphs and Running Graph Algorithms,'' Lecture
Notes in Computer Science, 2265 (2002), Springer
Verlag. (with A. Heinz).
- "Directed Polygons as
Boundaries of Visibility Graphs," Congressus Numerantium, 142
(2000), pp. 57-63. ( with John Emert and M. McGrew).
- "Hamiltonian Properties in
Bipartite Graphs," Bulletin of
the Institute
of Combinatorics and
its Applications, 26(1999). (with B. Varma)
- ``Independence and Cycles in Superline
Graphs,''Australasian Journal of
Combinatorics, 19 (1999). (with L. Beineke and B. Varma).
- ``The Super Line Graph L_2,''
Discrete Mathematics, 206 (1999) (with L. Beineke and B. Varma)
- ``Directed Polygons
Visibility Graphs,'' Congressus Numerantium, vol. 132, (1998), pp. 61-67.
( with John Emert and M. McGrew).
- ``The Complexity of
Illuminating Polygons by a-
floodlights,'' International Informatics Series 5, Canadian Conference
on Computational Geometry, 1996. (with L. Gewali and D. Glasser)
- ``Illuminating Simple
Polygons by Floodlights,'' Vision Geometry IV, The International
Society for Optical Engineering, 1995. (with L. Gewali and D. Glasser)
- ``The Line Completion Number
of a Graph,'' Graph Theory, Combinatorics, and Algorithms, John
Wiley, 1995. (with L. Beineke and B. Varma)
- ``Super Line Graphs, '' Graph
Theory, Combinatorics, and Algorithms, John Wiley, 1995. (with L.
Beineke and B. Varma)
- ``On the Pure Edge Integrity
of Graphs,'' Graph Theory, Combinatorics, and Algorithms, John
Wiley, 1995. (with J. Deogun)
- ``Edge Integrity - A
Survey,'' Discrete Applied Math, vol 124(1994), pp 3-12. (with L.
Beineke, M. Lipman, and R. Pippert)
- ``On the Sizes of Some
Visibility Graphs,'' Congressus Numerantium vol 104, 1994, pp 25-32. (with
J. Emert, M. McGrew, and W. Toll)
- ``Vertex Transitive Graphs of
Toughness One,'' The Bulletin of ICA,
10, 39-49, 1994. (with M. Lipman)
- ``Super Line Graphs and Their
Properties,'' in Proceedings of the Third China-USA International Graph
Theory Conference, Beijing,
1993. (with L. Beineke and B. Varma).
- ``The Super Line Graph L2 for
Hypercubes,'' Congressus Numerantium, vol 93, 1993, pp 111-113.
(with Maria Rosario Vasquez)
- ``On the Size of Minimal
Visibility Graphs,'' Department of Mathematical Sciences Technical Report
#87, Ball State University,
1993. (with M. McGrew, J. Emert, and W. Toll)
- ``Some Bounds and An
Algorithm for the Edge Integrity of Trees,'' Ars Combinatoria, 35-A, pp
225-238, 1993. (with L. Beineke, M. Lipman, and R. Pippert, and R. L.
Sedlmeyer)
- `` A Classification Scheme
for Vulnerability and Reliability Parameters of Graphs,'' Mathematical
and Computer Modeling, 17/11, 1993, pp13-16. (with L. Beineke, M.
Lipman, and R. Pippert)
- ``On the Honesty of Graph
Complements,'' Discrete Math, 122, pp 1--6, 1993. (with L. Beineke,
M. Lipman, and R. Pippert)
- ``A Survey of Integrity,'' Discrete
Applied Mathematics, vol 37-38, 1992, pp 13-28. (with L. Beineke, M.
Lipman, and R. Pippert)
- ``Two Problems on Coloring
Tournaments,'' Vishwa International Journal of Graph Theory, vol 1,
December 1992. (with L. Beineke and F. Harary)
- ``A Variation on the
Edge-Integrity,'' Congressus Numerantium, vol 91, 1992, pp207-211. (with
J. Deogun)
- ``Degree Conditions and Long
Cycles in Bipartite Graphs,'' Congressus Numerantium, vol 85, 1991, pp
123-128. (with B. Varma).
- ``Some Graph Theoretic
Properties of Petri Nets,'' Graph Theory, Combinatorics, and
Applications, vol 1, pp 19-28, John Wiley & Sons, 1991. (with F.
Owens)
- ``Extensions of an Algorithm
for Computing the Edge Integrity of Trees,'' Graph Theory,
Combinatorics, and Applications, vol 1, pp 41-54, John Wiley & Sons,
1991. (with L. Beineke, M. Lipman, R. Pippert)
- ``Petri Nets, State Machines
and Deadlocks'', ACM Nineteenth Annual Computer Science Conference,
March 1991. (Abstract) (with F. Owens)
- ``Bipartite Graphs and Degree
Conditions,'' Graph Theory, Combinatorics, Algorithms, and Applications
vol 54, SIAM,
1991. (with B. Varma)
- ``The Concept of Leverage in
Network Vulnerability,'' Graph Theory, Combinatorics, and Applications,
vol 1, pp 29-40, John Wiley & Sons, 1991. (with L. Beineke, M.
Lipman, R. Pippert)
- ``Explorations into Graph
Vulnerability,'' Graph Theory, Combinatorics, and Applications, vol 1,
pp 143-158, John Wiley & Sons, 1991. (with L. Beineke, M. Lipman,
R. Pippert)
- ``Low Dimensional Middle
Cubes are Hamiltonian,'' Computing in the 90's, Lecture Notes in
Computer Science #507, pp8-14, Springer Verlag, 1990. (with F. Owens)
- ``On Some Classes of Petri
Nets,'' ACM Eighteenth Annual Computer Science Conference, February
1990. (Abstract) (with F. Owens)
- ``On the Numbers of Some
Subtournaments of a Bipartite Tournament,'' Annals of the New York Academy of Sciences, vol 555, 1989.
(with L. W. Beineke)
- ``On Superstrong Tournaments
and Their Scores,'' Annals of the New York Academy
of Sciences, vol 555, 1989. (with L. W. Beineke)
- ``Deadlocks and Traps in
Complete Petri Nets,'' ACM Seventeenth Annual Computer Science
Conference, February 1989. (Abstract) (with F. Owens)
- ``A Good Algorithm for the
Computation of the Edge-Integrity of Trees,'' \it Congressus Numerantium,
vol 67, 1988, pp 225-232 (with L.W. Beineke, M.J. Lipman , R.E. Pippert ,
and R.L. Sedlmeyer)
- ``The Separation Sequence and
Network Reliability,'' Congressus Numerantium, vol 66 , 1988, pp 293-300
(with L.W. Beineke, M.J. Lipman , R.E. Pippert)
- ``Variations on a Theorem of
Petersen,'' Periodica Mathematica Hungarica, vol 19(3), 1988, pp.
241-247. (with L.W. Beineke, G. Chartrand, and O.R. Oellermann)
- ``On the Edge Integrity of
Graphs,'' Congressus Numerantium; vol 60, 1987, pp. 141-144. (with
L.W. Beineke, M.J. Lipman , R.E. Pippert)
- ``On Superstrong Bipartite
Tournaments,'' Congressus Numerantium, vol 53, 1987, pp. 113-119.
(with L. W. Beineke)
- ``Uniquely Realizable Score
Lists in Bipartite Tournaments,'' Czechoslovak Mathematical Journal,
vol 37, no. 112, 1987, pp. 323-333. (with L. W. Beineke)
- ``Some Results on Binary Matrices
Obtained via Bipartite Tournaments,'' in Graph Theory and its
Applications to Algorithms and Computer Science, John Wiley & Sons,
1985, pp. 47-56. (with L. W. Beineke)
- ``On Upsets in Bipartite
Tournaments,'' in Graph Theory and its Applications to Algorithms and
Computer Science, John Wiley & Sons, 1985, pp. 37-46.
Recent National and
International Presentations
- Workshop in Graph Theory, Algorithms,
and Applications, University of Yaounde I, Cameroon, September 7-11, 2009.
- (Invited Presentation) Frank Harary's Graph Theory in Games,
Tournaments and Social Networks (Annual Frank Harary Lecture Series), Department of Computer Science,
New Mexico State University, April 8, 2009.
- A Course in Graph Theory and its Applications, A three lecture course given
to researchers and fellows at United Nations University - International Institute for Software
Technology (UNU-IIST), Macau, China, March 17-23, 2009.
- (Invited Presentation) Graceful Labelings of Some Classes of Unicyclic Graphs -Properties and Algorithms,
Texas A&M University, Galveston, February 4, 2009.
- Graceful Labelings of Unicyclic Graphs,
International Conference on Discrete Mathematics (ICDM 2008), Mysore, India, June 6-10, 2008.
- Graceful Labelings:Properties and Algorithms at The Workshop in Some Recent Research
Directions in Graph Theory, May 26-30, 2008 at
Indian Institute of Technology, (IIT) Kharagpur, India.
- Properties of Graceful Labelings of Cycles, International Conference on Recent Developments
in Combinatorics and Graph Theory, Kalasalingam University, India, June 2007.
- Knowledge Management Software Systems in Academia and Industry, Invited presentation at the 94th
Indian Science Congress, Annamalai University, India, January 2007.
- Software Systems for Implementing Graph Algorithms for Learning
and Research, The First International Conference on Theories and Applications of
Computer Science (ICTACS '06), Vietnam, August 2006.
-
Model Checking with SPIN and its Industrial
Applications (Tutorial), ICTAC05 - International Colloquium on Theoretical
Aspects of Computing, Hanoi, Vietnam, October 2005.
- Some Structural Properties of Visibility Graphs, MIGHTY
XL Conference, Saginaw Valley State
University, Michigan,
April 2005.
- In Memory of Frank Harary, Thirty-Fifth Southeastern International
Conference on Combinatorics, Graph Theory, and Computing; Florida Atlantic
University, March 2005.
- Beineke and the Nine Commandments, MIGHTY
XXXIX Conference, Ball
State University,
November 2004.
- Applications of Formal
Methods to Industry, SERC Showcase, University
of Western Virginia, May
2004.
- Comparative Studies of Enrollment Patterns of Women in CS Programs:
Assessments and Recommendations, Women in Technology (WIT)
International Conference, Annamalai University, India, December 2003. (with Kim
Jones-Owen)
- Old and New Generalizations of Line Graphs, CombinaTexas: Combinatorics in the
South-Central U.S., April, 2003, Southwest Texas
State University.
- Some Properties of Triangle Graphs, Thirty-fourth Southeastern International
Conference on Combinatorics, Graph Theory, and Computing, Florida Atlantic
University, March, 2003.
- Formal Methods, Tools, and Applications to Industrial
Software Engineering, SERC
Formal Methods
Workshop Presentation, December 2002, Ball State University.
- Analysis of Relay Ladder Logic Programs, SERC (Software Engineering
Research Center) Showcase, West Virginia University, May 2002.
- Connectivity Properties of Visibility Graphs, 33rd Southeastern
International Conference on Combinatorics, Graph Theory, and Computing, Florida Atlantic University,
February 2002.
- RAISE - Rigorous Approach to Industrial Software Engineering, SERC (Software Engineering
Research Center)
Showcase, December 2001, Ball
State University.
- Bipairs of Bigraphs, Illinois Institute of Technology, Chicago, November 2001.
- Some New Results in Segment Endpoint Visibility Graphs, MIGHTY (Midwest
Graph Theory) XXXIV, October 2001, Oakland
University, Michigan.
- JGraph - A Java Based System for Drawing Graphs and Running Graph
Algorithms, Graph Drawing 2001 Conference, Vienna, Austria, September 2001.
- Visibility Graphs and Graph Drawing Algorithms. Series of four
lectures at UNU/IIST (United Nations University/International Institute for
Software Technology), August 2001.
- Fulbright Experience, Presentation at Fulbright Predeparture Orientation
Conference, Washington, DC, June 2001.
- Line Completion Numbers of Graphs, 32nd Southeastern International Conference
On Combinatorics, Graph Theory, and Computing, Louisiana State University, February 2001.
- Academic Differences: US vs. Zimbabwean Higher Education, US Embassy Public Affairs
Section Pre-Departure Orientation Program for Zimbabwean Students going to US,
July 2000.
- Toward the Development of a Production Management Subsystem, University
of Botswana International Conference
on Software Development, Gaborone,
Botswana, June
2000.
- Super Line Digraphs, Third International Conference on Combinatorial
Mathematics and Combinatorial Computing, University
of Melbourne, Australia,
July 1997.