Oral Presentations--Session 2Copyright (c) 2021 Illinois Wesleyan University All rights reserved.
https://digitalcommons.iwu.edu/jwprc/2014/oralpres2
Recent Events in Oral Presentations--Session 2en-usMon, 19 Apr 2021 14:03:33 PDT3600In Pursuit of the Ringel-Kotzig Conjecture: Uniform K-Distant Trees are Graceful
https://digitalcommons.iwu.edu/jwprc/2014/oralpres2/3
https://digitalcommons.iwu.edu/jwprc/2014/oralpres2/3Sat, 12 Apr 2014 10:00:00 PDT
Graph labeling has been an active area of research since 1967, when Rosa introduced the concept. Arguably, the biggest open conjecture in the field is referred to as the Ringel-Kotzig conjecture, which states that all trees admit a graceful labeling. In this talk, we will give a bit of background on the problem, as well as present our own results. Namely, that a certain infinite class of trees (called uniform k-distant trees) admits a graceful labeling.
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Kimberly Wenger et al.Bus Route Method and Isomorphism
https://digitalcommons.iwu.edu/jwprc/2014/oralpres2/2
https://digitalcommons.iwu.edu/jwprc/2014/oralpres2/2Sat, 12 Apr 2014 10:00:00 PDT
Two simple graphs, G and H, each of which have n vertices (with n a positive integer greater than 3) are called a graph pair of order n if the following three conditions all hold: (1) G and H union to the complete graph, (2) G and H have no isolated vertices, and (3) G is not isomorphic to H. Graph pairs of order 4 and 5 have been classified. This research took a step further to find graph pairs of order 6. During the finding, I discover the Bus Route method to make sure two graphs are not isomorphic. Two graphs G and H are said to be isomorphic if there exists a bijection, f, between the vertices of G and the vertices of H such that for every pair of vertices u and v in V(G), uv is an edge of G if and only if f(u)f(v) is an edge of H. The Bus Route method is based on the definition of isomorphism.
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Anh Phan et al.Construction of Spline Type Orthogonal Scaling Functions and Wavelets
https://digitalcommons.iwu.edu/jwprc/2014/oralpres2/1
https://digitalcommons.iwu.edu/jwprc/2014/oralpres2/1Sat, 12 Apr 2014 10:00:00 PDT
In this talk, we present a method to construct orthogonal spline-type wavelet. B-spline functions have several useful properties such as compactly support and refinement relationship. However, except for the case of the first order, B-splines of order greater than one are not orthogonal. To induce the orthogonality while keeping the properties of B-splines, we use a class of polynomial function factors to transform the original B-splines to a spline-type orthogonal compactly-supported and refinable scaling functions in L_{2}. In this paper we establish the existence of this class of polynomial factors and their construction. In addition, the corresponding spline-type wavelets and the decomposition and reconstruction formulas for their Multi-Resolution Analysis (MRA) are given.
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Tung Nguyen et al.