Oral Presentations--Session 11Copyright (c) 2021 Illinois Wesleyan University All rights reserved.
https://digitalcommons.iwu.edu/jwprc/2015/oralpres11
Recent Events in Oral Presentations--Session 11en-usMon, 19 Apr 2021 14:05:35 PDT3600An α-Labeling Walked into a Complete Graph…
https://digitalcommons.iwu.edu/jwprc/2015/oralpres11/3
https://digitalcommons.iwu.edu/jwprc/2015/oralpres11/3Sat, 18 Apr 2015 11:00:00 PDT
In 1967, Alex Rosa introduced multiple graph labelings useful for the purpose of studying decompositions. Since then, graph labeling has become a popular research topic independent of decompositions. In this talk, we return to the original purpose of two of Rosa’s labelings, the graceful labeling and the α-labeling, demonstrating their use in the study of decompositions. We also present a portion of our own results involving an extension of a class of trees called uniform k-distant trees; every tree in this new class of trees admits an α-labeling.
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Kimberly Wenger Diller et al.A Computational Study of Icart's Function
https://digitalcommons.iwu.edu/jwprc/2015/oralpres11/2
https://digitalcommons.iwu.edu/jwprc/2015/oralpres11/2Sat, 18 Apr 2015 11:00:00 PDT
A hash function maps elements of a larger, initial set into a smaller, resultant set. Sometimes, not all elements in the smaller set will be mapped to as a result; in general it is useful to know the size of this image. Here our target set is the points on an elliptic curve, which has an equation of the form y^2 = x^3 + ax + b. A hash function is useful here in offering a deterministic way to map an input to a pair of x and y values that satisfy such an equation. One such hash function was created by Thomas Icart. The researchers Fouque and Tibouchi provided a bound on the size of the image of Icart's output for curves defined over fields larger than 2^19. This research confirms their result for all fields and for many curves.
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Thomas Simmons et al.Multidecompositions of Complete Graphs into a Graph Pair of Order 6
https://digitalcommons.iwu.edu/jwprc/2015/oralpres11/1
https://digitalcommons.iwu.edu/jwprc/2015/oralpres11/1Sat, 18 Apr 2015 11:00:00 PDT
A graph is a mathematical structure consisting of a set of objects called vertices and a set of 2-element subsets of vertices, called edges. The complete graph on n vertices is the graph with n vertices and an edge between any pair of distinct vertices. Let C_{6} denote the cycle on 6 vertices. We are interested in partitioning the edges of the complete graph on n verticesinto copies of C_{6} and its complement with at least one copy of each graph. We provide necessary and sufficient conditions on n for the existence such a structure.
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Yizhe Gao et al.