# Welcome to the Office of Graduate Studies &Postdoctoral Fellows

### Upcoming Events

• Shari Worsfold, EdD Thesis Examination
9:30 AM - 12:30 PM
November 30, 2015
Student: Shari Worsfold Degree: EdD Thesis Title: Supporting Classroom Literacy Instruction for Vulnerable Learners with Reflective Dialogue Senior Supervisor: Allan MacKinnon Please see the Graduate Studies website for more details: http://www.sfu.ca/education/gs/current-students/thesisexaminations.html
• Andrew La Croix, PhD Thesis Defence, Earth Sciences
1:00 PM - 4:00 PM
November 30, 2015
Title: "Modern and Ancient Perspectives on Deposition Across the Tidal– Fluvial Transition in Rivers " For further information please contact the Graduate secretary at eascgsec@sfu.ca
• Tomas Boothby - PhD Defence
3:00 PM - 6:00 PM
November 30, 2015
We present three results. The first is a result in structural graph theory. It demonstrates a large family of complete graphs embedded (clique embeddings) as minors of the grid-like Chimera graph, which is an abstract graph representing the D-Wave quantum adiabatic processor where vertices of the Chimera graph represent qubits in the processor. These particular embeddings are uniform in the sense that each vertex of the complete graph is represented by an equal number of vertices in the Chimera graph, which is thought to improve performance of the D-Wave processor. We present a polynomial-time algorithm to find a largest clique in this family in arbitrary induced subgraphs. Then we use the output of our algorithm as a measure of quality of a particular induced subgraph and show that the size of the largest clique embedding grows logarithmically in the grid size when a fixed percentage of qubits have been deleted. The second is a result in design theory and combinatorial number theory. We construct a family of designs called Heffter arrays. A Heffter array is a $(m \times n)$ integer matrix whose entries' absolute values cover the interval $[1,mn]$, where every row and column sums to zero modulo $2mn+1$. Archdeacon uses Heffter arrays to construct embeddings of the complete graph $K_{2mn+1}$ into orientable surfaces such that every edge appears in an $m$-cycle and an $n$-cycle, provided either $m$ or $n$ is odd. We prove that $m \times n$ Heffter arrays exist if and only $m>2$ and $n>2$. The third is a result in combinatorial number theory and structural graph theory. For subsets $A,B$ of a group $G$ define the product set $AB = \{ab : a \in A, b \in B\}$. We classify the sets $A,B$ such that $|AB| \leq |A|+|B|$ when $B$ is the union of two $H$ cosets by reducing the problem to, and classifying, vertex- and edge-transitive $d$-regular graphs with edge cuts of size at most $2d$. Along the way, we classify $d$-regular vertex- and edge-transitive graphs with girth $g$ such that $dg \leq 2(d+g)$: with a provided finite list of exceptions, each edge belongs to at most two $g$-cycles. Sr Supr: Matt DeVos Committee: Petr Lisonek Title: Some Results on Structure in Graphs and Numbers

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