Mathematics Commons^™

Categorical Aspects Of Graphs, Jacob D. Ender

Undergraduate Student Research Internships Conference

In this article, we introduce a categorical characterization of directed and undirected graphs, and explore subcategories of reflexive and simple graphs. We show that there are a number of adjunctions between such subcategories, exploring varying combinations of graph types.

Analysing Flow Free With One Pair Of Dots, Eliot Harris Roske

Senior Projects Spring 2019

Flow Free is a smartphone puzzle game where the player is presented with an m by m grid containing multiple pairs of colored dots. In order to solve the puzzle, the player must draw a path connecting each pair of points so that the following conditions are met: each pair of dots is connected by a path, each square of the grid is crossed by a path, and no paths intersect. Based on these puzzles, this project looks at grids of size m by n with only one pair of dots to determine for which configurations of dots a solution …

Exploring Tournament Graphs And Their Win Sequences, Sadiki O. Lewis

Senior Projects Fall 2016

In this project we will be looking at tournaments on graphs and their win sequences. The main purpose for a tournament is to determine a winner amongst a group of competitors. Usually tournaments are played in an elimination style where the winner of a game advances and the loser is knocked out the tournament. For the purpose of this project I will be focusing on Round Robin Tournaments where all competitors get the opportunity to play against each other once. This style of tournaments gives us a more real life perspective of a fair tournament. We will model these Round …

Groups As Graphs, Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

Through this book, for the first time we represent every finite group in the form of a graph. The authors choose to call these graphs as identity graph, since the main role in obtaining the graph is played by the identity element of the group. This study is innovative because through this description one can immediately look at the graph and say the number of elements in the group G which are self-inversed. Also study of different properties like the subgroups of a group, normal subgroups of a group, p-sylow subgroups of a group and conjugate elements of a group …

Maps Which Preserve Graphs, Van C. Nall

Department of Math & Statistics Faculty Publications

In 1976 Eberhart, Fúgate, and Gordh proved that the weakly confluent image of a graph is a graph. A much weaker condition on the map is introduced called partial confluence, and it is shown that the image of a graph is a graph if and only if the map is partially confluent.

In addition, it is shown that certain properties of one-dimensional continua are preserved by partially confluent maps, generalizing theorems of Cook and Lelek, Tymchatyn and Lelek, and Grace and Vought. Also, some continua in addition to graphs are shown to be the images of partially confluent maps only.