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Full-Text Articles in Other Mathematics

Strong Neighborhood-Prime Labelings Under Ordinary & Gaussian Integers, Micheal Arnal-Brown Jan 2025

Strong Neighborhood-Prime Labelings Under Ordinary & Gaussian Integers, Micheal Arnal-Brown

Murray State Theses and Dissertations

This thesis introduces and studies the notion of a strong neighborhood-prime labeling, a strengthening of the neighborhood-prime labeling where the label 1 can be assigned to any vertex in a graph. We prove that several graph families—including paths, cycles (excluding those congruent to 2 modulo 4), caterpillars, helm graphs, closed helm graphs, gear graphs, and graphs with universal vertices—admit such labelings, and also provide results to more general classes of graphs. We extend this new labeling concept to the Gaussian integers using a spiral order- ing on Z[i] and define a Gaussian analogue of strongly neighborhood-primeness. To support this extension, …


Kōlams In Graph Theory: Mathematics In South Indian Ritual Art, Nathan Hartmann Jan 2023

Kōlams In Graph Theory: Mathematics In South Indian Ritual Art, Nathan Hartmann

Murray State Theses and Dissertations

Kōlams are a ritual art form found in India, most commonly in the southern state
of Tamil Nadu. Comprised of different interlocking knots, these women-drawn designs are placed on the entrances to people’s home to showcase the household’s emotional state and ask the earth goddess Bhūdevi for forgiveness. More aesthetically pleasing kōlams are considered latshanam, where the design permeates beauty; monolinearity is one such aspect that implements latshanam. Using graph theory, we examine one style of these drawings, the labyrinthine variety, to identify if a given kōlam is monolinear and how to construct monolinear kōlams.


Grim Under A Compensation Variant, Aaron Davis, Aaron Davis Nov 2020

Grim Under A Compensation Variant, Aaron Davis, Aaron Davis

Honors College Theses

Games on graphs are a well studied subset of combinatorial games. Balance and strategies for winning are often looked at in these games. One such combinatorial graph game is Grim. Many of the winning strategies of Grim are already known. We note that many of these winning strategies are only available to the first player. Hoping to develop a fairer Grim, we look at Grim played under a slighlty different rule set. We develop winning strategies and known outcomes for this altered Grim. Throughout, we discuss whether our altered Grim is a fairer game then the original.


Evaluating An Ordinal Output Using Data Modeling, Algorithmic Modeling, And Numerical Analysis, Martin Keagan Wynne Brown Jan 2020

Evaluating An Ordinal Output Using Data Modeling, Algorithmic Modeling, And Numerical Analysis, Martin Keagan Wynne Brown

Murray State Theses and Dissertations

Data and algorithmic modeling are two different approaches used in predictive analytics. The models discussed from these two approaches include the proportional odds logit model (POLR), the vector generalized linear model (VGLM), the classification and regression tree model (CART), and the random forests model (RF). Patterns in the data were analyzed using trigonometric polynomial approximations and Fast Fourier Transforms. Predictive modeling is used frequently in statistics and data science to find the relationship between the explanatory (input) variables and a response (output) variable. Both approaches prove advantageous in different cases depending on the data set. In our case, the data …


An Application Of A Binary-Integer Programming Process To The Faculty-Course Assignment Problem, Charles Graves Jan 2020

An Application Of A Binary-Integer Programming Process To The Faculty-Course Assignment Problem, Charles Graves

Murray State Theses and Dissertations

Have you ever wondered why you have a certain class or professor at a certain time during the week? Creating a faculty-course schedule is a complicated and time- consuming process. In this thesis, we will examine two binary-integer programming models to generate the faculty-course schedule with various unique course preparations for the Department of Mathematics and Statistics at Murray State University. The first model will present a traditional, on-campus course schedule, and the second will present an online, asynchronous learning course schedule.


Correlations Of Co2 Levels, Brittney Nelson Apr 2018

Correlations Of Co2 Levels, Brittney Nelson

Scholars Week

This project looks at the correlation between CO2 levels and human influences as well as the correlation between CO2 levels and global temperatures.


Distributive Lattice Models Of The Type B Elementary Weyl Group Symmetric Functions, Katheryn Beck Jan 2018

Distributive Lattice Models Of The Type B Elementary Weyl Group Symmetric Functions, Katheryn Beck

Murray State Theses and Dissertations

One of the great themes of algebraic combinatorics is the exploration of connections between ordered structures and group actions/representations. This thesis furthers this theme by presenting diamond-colored distributive lattice models of certain poly nomials that are invariant under the action of the type Bn Weyl group. Initially we realize these lattices as diamond-colored lattices of order ideals from certain vertex colored posets. We explore various coordinatizations of these lattices via partition-like elements, tableaux, and binary-type representations called tally diagrams. We also examine algebraic properties of these lattices. In particular, we prove that our type Bn lattices are effective models for …


Distributive Lattice Models Of The Type C One-Rowed Weyl Group Symmetric Functions, William Atkins Jan 2018

Distributive Lattice Models Of The Type C One-Rowed Weyl Group Symmetric Functions, William Atkins

Murray State Theses and Dissertations

We present two families of diamond-colored distributive lattices – one known and one new – that we can show are models of the type C one-rowed Weyl symmetric functions. These lattices are constructed using certain sequences of positive integers that are visualized as filling the boxes of one-rowed partition diagrams. We show how natural orderings of these one-rowed tableaux produce our distributive lattices as sublattices of a more general object, and how a natural coloring of the edges of the associated order diagrams yields a certain diamond-coloring property. We show that each edge-colored lattice possesses a certain structure that is …


Neural Network Predictions Of A Simulation-Based Statistical And Graph Theoretic Study Of The Board Game Risk, Jacob Munson Jan 2017

Neural Network Predictions Of A Simulation-Based Statistical And Graph Theoretic Study Of The Board Game Risk, Jacob Munson

Murray State Theses and Dissertations

We translate the RISK board into a graph which undergoes updates as the game advances. The dissection of the game into a network model in discrete time is a novel approach to examining RISK. A review of the existing statistical findings of skirmishes in RISK is provided. The graphical changes are accompanied by an examination of the statistical properties of RISK. The game is modeled as a discrete time dynamic network graph, with the various features of the game modeled as properties of the network at a given time. As the network is computationally intensive to implement, results are produced …