Department of Math & CS 

Address: 
Joy Morris Department of Mathematics & Computer Science University of Lethbridge 4401 University Drive Lethbridge, AB CANADA T1K 3M4 

Teaching Activities 
Fall 2024  
Math 3860, Section A  
Math 4405, Section A 
Spring 2025  Summer 2025  
(no teaching duties) 
Open Access Text Books  
Proofs and Concepts  
coauthored with Dave Morris. An undergraduate text book introducing proof techniques. We use this for a 2ndyear university course.  
Combinatorics  
An upperlevel undergraduate text book for an introductory course in combinatorics, including enumeration, graph theory, and design theory. We use this for a 3rdyear university course. 
Parent Math Help DropIn  
In 2017 I worked with Lethbridge School District 51 and PS 2 Math Education students at the University of Lethbridge to hold an 8week dropin program. This program was a help session for parents who were seeking help in understanding the math their children are learning, or who are looking for fun activities that will help their children learn to achieve middle school math outcomes (from the Alberta curriculum). We reached an estimated 100 individuals over the course of the program. A video about these sessions is available on YouTube, through this link. There have been subsequent sessions in 2018 (see this Global News video), 2019 (see this Lethbridge Herald article), and 2020. 
Research Activities 
Connectivity of Cayley Graphs: A Special Family  (Appeared in JCMCC, 1996) 
Isomorphic Cayley Graphs on different Groups  (Appeared in Congressus Numerantium, 1996) 
Automorphism groups with Cyclic Commutator Subgroups and Hamilton Cycles  (With E. Dobson, H. Gavlas and D. Witte. Appeared in Discrete Math., 1998) 
Isomorphic Cayley Graphs on Nonisomorphic Groups  (Appeared in JGT, 1999) 
Selfcomplementary Circulant Graphs  (With B. Alspach and V. Vilfred. Appeared in Ars Combinatoria, 1999) 
Classifying ArcTransitive Circulants of Squarefree Order  (With C. H. Li and D. Marusic. Appeared in JACO, 2001) 
Toida's Conjecture is True  (With E. Dobson. Appeared in Electronic J. of Combin., 2002) 
Results towards showing Z_p^n is a CIgroup  (Appeared in Congressus Numerantium, 2002) 
Stitching Images Back Together  (With F. Lutscher, J. McNulty, and K. Seyffarth. Appeared in Congressus Numerantium, 2003) 
On automorphism groups of circulant digraphs of squarefree order  (With E. Dobson. Appeared in Discrete Math., 2005) 
Flows that are sums of hamiltonian cycles in Cayley graphs on abelian groups  (With D. Morris and D. Moulton. Appeared in Discrete Math., 2005) 
Brian Alspach and his work  (With M. Sajna. Appeared in Discrete Math., 2005) 
Normal circulant graphs with noncyclic regular subgroups  (With D. Marusic. Appeared in JGT, 2005) 
Automorphism groups of circulant graphs  a survey  (Appeared in Graph Theory, Trends in Math., Birkhauser, 2006) 
Cyclic hamiltonian cycle systems of the complete graph minus a 1factor  (With H. Jordon. Appeared in Discrete Math., 2008) 
Automorphism groups of wreath product digraphs  (With E. Dobson. Appeared in Electronic J. of Combin., 2009) 
Directed cyclic hamiltonian cycle systems of the complete symmetric digraph  (With H. Jordon. Appeared in Discrete Math., 2009) 
Hamiltonian cycles in (2,3,c)circulant digraphs  (With D. Morris and K. Webb. Appeared in Discrete Math., 2009) 
Strongly regular edgetransitive graphs  (With C. Praeger and P. Spiga. Appeared in Ars Mathematica Contemporanea, 2009) 
Balanced Cayley graphs and balanced planar graphs  (With P. Spiga and K. Webb. Appeared in Discrete Math., 2010) 
Hamiltonian cycles in Cayley graphs whose order has few prime factors  (With K. Kutnar, D. Marusic, D. Morris and P. Sparl. Appeared in Ars Mathematica Contemporanea, 2012.) 
Cayley graphs of order 16p are hamiltonian  (With S. Curran and D. Morris. Appeared in Ars Mathematica Contemporanea, 2012.) 
Generalised quadrangles with a group of automorphisms acting primitively on points and lines  (With J. Bamberg, M. Giudici, G. Royle and P. Spiga. Appeared in J. Combin. Theory  A, 2012.) 
On the automorphism groups of almost all circulant graphs and digraphs  (With S. Bhoumik and E. Dobson. Appeared in Ars Math. Comtemp., 2014.) 
Automorphisms of Cayley graphs on generalised dicyclic groups,  (With P. Spiga and G. Verret. Appeared in Europ. J. Combin., 2015.) 
Affine transformations of finite vector spaces with large orders or few cycles,  (With S. Guest, C. Praeger, and P. Spiga. Appeared in J. Pure and Applied Alg., 2015.) 
Elementary proof that (Z_p)^4 is a DCIgroup.  (Appeared in Discrete Math., 2015.) 
Quotients of CIgroups are CIgroups,  (With E. Dobson. Appeared in Graphs and Combin., 2015.) 
Semiregular automorphisms of cubic vertextransitive graphs and the abelian normal quotient method,  (With P. Spiga and G. Verret. Appeared in Electronic. J. Combin., 2015.) 
On colourpreserving automorphisms of Cayley graphs,  (With A. Hujdurovic, K. Kutnar, and D. Morris. Appeared in Ars. Math. Contemp., 2015.) 
On the maximum orders of elements of finite almost simple groups and primitive permutation groups,  (With S. Guest, C. Praeger, and P. Spiga. Appeared in Trans. Amer. Math. Soc., 2015.) 
Further restrictions on the structure of finite DCIgroups: an addendum,  (With E. Dobson and P. Spiga. Appeared in J. Alg. Combin., 2015.) 
Λtransitive digraphs preserving a cartesian decomposition  (With P. Spiga. Appeared in J. of Australian Math. Sci., 2015.) 
Finite primitive permutation groups containing a permutation having at most four cycles,  (With S. Guest, C. Praeger, and P. Spiga. Appeared in J. Alg., 2016.) 
Automorphisms of circulants that respect partitions,  (Appeared in Contributions to Discrete Math., 2016.) 
Isomorphisms of Cayley graphs on nilpotent groups,  (With D. Morris and G. Verret. Appeared in New York J. Math., 2016.) 
The CI problem for infinite groups,  (Appeared in Electronic J. Combin., 2016.) 
Vertextransitive digraphs with extra automorphisms that preserve the natural arccolouring,  (With E. Dobson, A. Hujdurovic, and K. Kutnar. Appeared in Australasian J. Combin., 2017.) 
Cyclic mCycle Systems of Complete Graphs minus a 1factor,  (With H. Jordon. Appeared in Australasian J. Combin., 2017.) 
On Color Preserving Automorphisms of Cayley Graphs of Odd Squarefree Order,  (With E. Dobson, A. Hujdurovic, and K. Kutnar. Appeared in J. Alg. Combin., 2017) 
Every finite nonsolvable group admits an Oriented Regular Representation,  (With P. Spiga. Appeared in by J. Combin. Theory  B, 2017.) 
Characterising CCA Sylow cyclic groups whose order is not divisible by four,  (With L. Morgan and G. Verret. Appeared in Ars Math. Contemp., 2018) 
Most Rigid Representations and Cayley Index,  (With J. Tymburski. Appeared in Art of Disc. and App. Math., 2018) 
Automorphism groups of circulant digraphs with applications to semigroup theory,  (With J. Araujo, W. Bentz, E. Dobson, and J. Konieczny. Appeared in Combinatorica, 2018.) 
Classification of finite groups that admit an oriented regular representation,  (With P. Spiga. Appeared in Bull. London Math. Soc., 2018) 
Digraphs with small automorphism groups that are Cayley on two nonisomorphic groups,  (With L. Morgan and G. Verret. Appeared in Art of Disc. and App. Math., 2020) 
A finite simple group is CCA if and only if it has no element of order four,  (With L. Morgan and G. Verret. Appeared in J. Algebra, 2021) 
Asymptotic enumeration of Cayley digraphs,  (With P. Spiga. Appeared in Israel J. Math., 2021) 
Two new families of nonCCA groups,  (With B. Fuller. Appeared in Art of Disc. and App. Math., 2021) 
Two families of graphs that are Cayley on nonisomorphic groups,  (With J. Smolcic. Appeared in J. Alg., Comb., Disc. Structures, and Apps., 2021) 
Cayley graphs of more than one abelian group,  (With E. Dobson. Appeared in Art of Disc. and App. Math., 2021) 
On the asymptotic enumeration of Cayley graphs,  (With M. Moscatiello and P. Spiga. Appeared in Ann. di Math. Pura e App., 2021) 
Groups for which it is easy to detect graphical regular representations,  (With D. Morris and G. Verret. Appeared in Art of Disc. and App. Math., 2022) 
Most generalized Petersen graphs of girth 8 have cop number 4,  (With T. Runte and A. Skelton. Appeared in Australasian J. Combin., 2022) 
On generalised Petersen graphs of girth 7 that have cop number 4,  (With H. Morris. Appeared in Art of Disc. and App. Math., 2022) 
Induced forests in some distanceregular graphs,  (With K. Gunderson, K. Meagher, and V. Pantangi. Appeared in Disc. App. Math., 2024) 
(Z_3)^8 is not a CIgroup  (Accepted by Ars Math. Contemp.) 
Classification of vertextransitive digraphs via automorphism group,  (With E. Dobson, A. Hujdurovic, and K. Kutnar. Submitted to Electronic J. Combin.) 
NonCayleyIsomorphic Cayley graphs from nonCayleyIsomorphic Cayley digraphs,  (With D. Morris. Accepted by Australasian J. Combin.) 
Detecting graphical and digraphical regular representations in groups of squarefree order,  (With G. Verret. Submitted to Electronic J. Combin.) 
Dihedral groups of order 2pq or 2pqr are DCI  (Submitted to Ars Math. Contemp.) 
Haar graphical representations of finite groups and an application to poset representations,  (With P. Spiga. Submitted to J. Combin. Theory  B.) 
Groups with elements of order 8 do not have the DCI property,  (With E. Dobson and P. Spiga. Submitted to Art of Disc. and App. Math.) 
Robustness of ErdosKoRado theorems on permutations and perfect matchings,  (With K. Gunderson, K. Meagher, V. Pantangi, and M. Shirazi. Submitted to Forum Sigma.) 
(Note: Dates inside the early files represent the dates on which I converted them to .pdf form, and may bear no relation to their publication dates. The
files are not usually the final published version of the paper, due to copyright issues.)
Here are slides from the plenary talk I gave at the 8th Slovenian Conference on Graph Theory, June 2015. I have removed most of the page breaks from the slides.
I married Dave Morris in December of 2002. Here is a wedding photo.