Global ETD Search
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Showing 1 to 20 of 56 for “"Discrete Mathematics and Combinatorics"”.
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Irreducible Representations from Group Actions on Trees
… $S_n$ found by acting on</p> <p>labeled graphs and trees with $n$ vertices. Our main results provide</p> <p>combinatorial interpretations that give the number of times the irreducible</p> <p>representations associated with the integer partitions $(n)$ and $(1^n)$ appear</p> <p>in the …
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Theory and application of back-tracking techniques
… However, the size of the problem that can be handled is limited by the speed and by the accessibility of the computer. Back-tracking is a technique that provides a more efficient method of solving such problems, and thus enables larger problems to he handled.</p> <p>Chapter I introduces the …
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Error correcting binary codes
… is the "encoding problem." In Chapters 1, 2, 3, and 5, we are primarily concerned with linear codes in which the encoder is a linear transformation of then dimensional vector space containing the message vectors into the vector space of dimension n + k, such that certain errors can be located or …
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PLANAR GRAPHS, BIPLANAR GRAPHS AND GRAPH THICKNESS
… that no two edges cross. The smallest complete and complete bipartite graphs that are not planar are K5 and K{3,3}. A biplanar graph is a graph whose edges can be colored using red and blue such that the red edges induce a planar subgraph and the blue edges induce a planar subgraph. In this …
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Modeling repairable system failure data using NHPP reliability growth mode.
… the intensity function of the power law model, and so the log-linear model was fitted and tested for goodness-of-fit. The Weibull Time to Failure recurrent neural network (WTTE-RNN) framework, a probabilistic deep learning model for failure data, is also explored. However, we find that the …
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Upset Paths and 2-Majority Tournaments
… they proved that when a majority means that Candidate A beats Candidate B when Candidate A is ranked above Candidate B by at least two out of three voters, the tournament used to model this voting scenario has a minimum dominating set of size at most three. This result gives 2-majority …
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Diederich-Fornæss Index on Boundaries Containing Crescents
<p>The worm domain developed by Diederich and Fornæss is a classic example of a boundedpseudoconvex domains that fails to satisfy global regularity of the Bergman Projection, due to the set of weakly pseudoconvex points that form an annulus in its boundary. We instead examine a bounded pseudoconvex …
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From Simplest Recursion to the Recursion of Generalizations of Cross Polytope Numbers
… investigations in the mathematical field of combinatorics. The research study will be based on the results of Professors Steven Edwards and William Griffiths, who recently found a new formula for the cross-polytope numbers. My topic will be focused on "Generalizations of cross-polytope …
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Precise Partitions Of Large Graphs
… help us in rest of this thesis. In 2000, Enomoto and Ota posed a conjecture on the existence of path decomposition of graphs with fixed start vertices and fixed lengths. We prove this conjecture when |G| is large. Our proof uses the Regularity Lemma along with several extremal lemmas, concluding …
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Utilization of Partitions in Graph Structures
… types of graphs. Gallai-Ramsey problems and conjectures which require the Regularity lemma require unique methods to improve the bounds on known results. In this work the upper bounds for Gallai-Ramsey using $k$ colors is lowered to at most $k(n-1) +3n$ for even cycles and $(2^{k+3}-3)n …
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Zero Sets in Graphs.
… but adjacent to vertices in <em>S</em>, and the cardinality of the set <em>S</em>. The <em>differential of a graph G</em> equals the maximum differential of any subset <em>S</em> of <em>V</em> . A set <em>S</em> is called a <em>zero set</em> if ∂(<em>S</em>) = 0. In this thesis we …
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The Linear Cutwidth and Cyclic Cutwidth of Complete n-Partite Graphs
… we strictly consider the linear embedding and cyclic embedding. The relationship between the linear cutwidth and the cyclic cutwidth is discussed and used throughout multiple proofs of different cases for the cyclic cutwidth. All the known cases for the linear and cyclic cutwidth of …
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Expectation Numbers of Cyclic Groups
<p>When choosing k random elements from a group the kth expectation number is the expected size of the subgroup generated by those specific elements. The main purpose of this thesis is to study the asymptotic properties for the first and second expectation numbers of large cyclic groups. The first …
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Graphs of Classroom Networks
… a representation of the students in a classroom, and we use the number of peers with whom a student studied or collaborated to determine the degree of each. We expand upon the Havel-Hakimi algorithm by coding a program in MATLAB that generates random graphs with the same degree sequence. Then, we …
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Extremal Graph Theory and Enumerative Combinatorics
… the tree) two different `middle points' can be and when such maximum distances are achieved. We also naturally extended to trees with restricted degrees or diameter. The second topic is about trees with given degree sequence in S-order. The first trees in S-order with the additional condition …
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Omnisculptures.
… recent work conducted on one dimensional and two dimensional patterns known as omnisequences and omnimosaics, respectively. These have been studied by Abraham et al [3] and Banks et al [2]. The three dimensional patterns we study are called omnisculptures, and will be the focus of this …
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Peg Solitaire on Trees with Diameter Four
<p>In a paper by Beeler and Hoilman, the traditional game of peg solitaire is generalized to graphs in the combinatorial sense. One of the important open problems in this paper was to classify solvable trees. In this thesis, we will give necessary and sufficient conditions for the solvability for …
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Very Cost Effective Partitions in Graphs
<p>For a graph G=(V,E) and a set of vertices S, a vertex v in S is said to be very cost effective if it is adjacent to more vertices in V -S than in S.</p> <p>A bipartition pi={S, V- S} is called very cost effective if both S and V- S are very cost effective sets. Not all graphs have a very cost …
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