The reconstruction of maximal planar graphs II. Reconstruction

AbstractIn the first paper [3], the author, together with Fiorini, has shown that maximal planar graphs are recognizable from their decks of vertex-deleted subraphs. The aim of this paper is to show that such graphs are reconstructible

The reconstruction of planar graphs

The object of this thesis is to investigate the Reconstruction Problem for planar graphs. This study naturally leads to related topics concerning certain nonplanar graphs and the use of their embeddings on appropriate surfaces to reconstruct them. The principal aim of this work is to find new techniques of reconstruction and to increase the number of classes of graphs known to be reconstructible. In achieving this aim, various important properties of graphs, such as connectivity and uniqueness of embeddings, are explored, and new results on these topics are obtained. Part I, which consists of three chapters, contains a historic a l, non-technical introduction and general graph-theoretical definitions, notation and results. Some new concepts in reconstruction are also presented, notably the idea of reconstructor sets. Part II of the thesis deals with the vertex-reconstruction of maximal planar graphs: Chapter 4 is concerned with the vertex-recognition of maximal planarity, whereas Chapter 5 deals with the vertex-reconstruction. Part III deals with edge-reconstruction: planar graphs with minimum valency 5 and 4-connected planar graphs are reconstructed in Chapters 6 and 7 respectively. In Chapter 7, extensive use is made of the concept of reconstructor sets introduced in Chapter 3. This chapter also contains a brief discussion on the reconstruction of graphs from edge-contracted subgraphs, a problem which, in certain cases, can be regarded as dual to the Edge-reconstruction Problem. Part IV is concerned with extending the results and techniques of the previous chapters to nonplanar graphs. Chapter 8 discusses where the previous techniques fa il, and indicates where new methods are needed. In Chapter 9, all graphs which triangulate some surface and have connectivity 3 are edge-reconstructed. Certain graphs which triangulate the torus or the projective plane are also shown to be weakly vertex-reconstructible. Chapter 10 deals with the edge-reconstruction of all graphs which triangulate the projective plane. The Appendix proves a conjecture of Harary on the cutvertex-reconstruction of trees. One technique used here ties up with a method employed in previous chapters on edge-reconstruction

Braiding Interactions in Anyonic Quantum Walks

The anyonic quantum walk is a dynamical model describing a single anyon propagating along a chain of stationary anyons and interacting via mutual braiding statistics. We review the recent results on the effects of braiding statistics in anyonic quantum walks in quasi-one dimensional ladder geometries. For anyons which correspond to spin-1/2 irreps of the quantum groups $SU(2)_k$, the non-Abelian species $(1<k<\infty)$ gives rise to entanglement between the walker and topological degrees of freedom which is quantified by quantum link invariants over the trajectories of the walk. The decoherence is strong enough to reduce the walk on the infinite ladder to classical like behaviour. We also present numerical results on mixing times of $SU(2)_2$ or Ising model anyon walks on cyclic graphs. Finally, the possible experimental simulation of the anyonic quantum walk in Fractional Quantum Hall systems is discussed.Comment: 13 pages, submitted to Proceedings of the 2nd International Conference on Theoretical Physics (ICTP 2012

Education, Exploration and the Elephant in the Room: A Narrative Inquiry of Sexuality and Sex Education among Adolescents with Physical Disabilities

Guided by a constructivist paradigm, this qualitative research study used a multidimensional form of narrative inquiry in order to understand the experiences of learning about sexuality among adolescents with physical disabilities, and in turn, how these experiences influence the way they view themselves as sexual beings. For the purposes of this research, in-depth narrative interviews were conducted with adolescents who have physical disabilities and parents of youth with physical disabilities, as well as a focus group with health professionals. The findings from this study demonstrate that these adolescents often face challenges in accessing disability- specific sex information due to a lack of appropriate resources, discomfort with the topic among educators, health professionals and parents, as well as the pervasive social myth that views people with disabilities as asexual. The data from this study contributes to the literature about sexuality among adolescents with physical disabilities by drawing attention to this important but often overlooked issue, as well as offering recommendations for future resource development that could help empower these youth with the knowledge and skills needed to engage in safe, healthy and fulfilling relationships

Student and faculty expectations for learning in various delivery models

The purpose of this presentation is to shed light on expectations and characteristics of both students and faculty with the hope of improving the learning experience for all by minimizing frustrations and clarifying each others roles. We do much of this already, but it’s nice to have a reminder, and maybe a different take on some ideas

Examining the Why: The relevance of our courses

If we want students to be truly engaged, not just doing enough to get a passing grade, we need to make sure they make a connection between our course content and their future