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Full-Text Articles in Physical Sciences and Mathematics
Finite Simple Graphs And Their Associated Graph Lattices, James B. Hart, Brian Frazier
Finite Simple Graphs And Their Associated Graph Lattices, James B. Hart, Brian Frazier
Theory and Applications of Graphs
In his 2005 dissertation, Antoine Vella explored combinatorical aspects of finite graphs utilizing a topological space whose open sets are intimately tied to the structure of the graph. In this paper, we go a step further and examine some aspects of the open set lattices induced by these topological spaces. In particular, we will characterize all lattices that constitute the opens for finite simple graphs endowed with this topology, explore the structure of these lattices, and show that these lattices contain information necessary to reconstruct the graph and its complement in several ways.
Unavoidable Immersions And Intertwines Of Graphs, Matthew Christopher Barnes
Unavoidable Immersions And Intertwines Of Graphs, Matthew Christopher Barnes
LSU Doctoral Dissertations
The topological minor and the minor relations are well-studied binary relations on the class of graphs. A natural weakening of the topological minor relation is an immersion. An immersion of a graph H into a graph G is a map that injects the vertex set of H into the vertex set of G such that edges between vertices of H are represented by pairwise-edge-disjoint paths of G. In this dissertation, we present two results: the first giving a set of unavoidable immersions of large 3-edge-connected graphs and the second on immersion intertwines of infinite graphs. These results, along with …
On Some Geometry Of Graphs, Zachary S. Mcguirk
On Some Geometry Of Graphs, Zachary S. Mcguirk
Dissertations, Theses, and Capstone Projects
In this thesis we study the intrinsic geometry of graphs via the constants that appear in discretized partial differential equations associated to those graphs. By studying the behavior of a discretized version of Bochner's inequality for smooth manifolds at the cone point for a cone over the set of vertices of a graph, a lower bound for the internal energy of the underlying graph is obtained. This gives a new lower bound for the size of the first non-trivial eigenvalue of the graph Laplacian in terms of the curvature constant that appears at the cone point and the size of …
Exploring Sequences Of Tournament Graphs With Draws, Kaylynn H. Tran
Exploring Sequences Of Tournament Graphs With Draws, Kaylynn H. Tran
Senior Projects Spring 2018
Tournaments occur all over the world and they are used to decide championships in various competitions. For this project, I will be exploring tournaments in the round robin style in which every team plays one another. This is based on Sadiki Lewis' senior project, Exploring Tournament Graphs and Their Win Sequences. I will be expanding his project by including the possibility of a draw between two teams, in addition to a win or a loss. Teams and games will be modeled by complete graphs where each vertex represents a team and each directed edge between two vertices represents the outcome …
Graph Homomorphisms And Vector Colorings, Michael Robert Levet
Graph Homomorphisms And Vector Colorings, Michael Robert Levet
Theses and Dissertations
A graph vertex coloring is an assignment of labels, which are referred to as colors, such that no two adjacent vertices receive the same color. The vertex coloring problem is NP-Complete [8], and so no polynomial time algorithm is believed to exist. The notion of a graph vector coloring was introduced as an efficiently computable relaxation to the graph vertex coloring problem [7]. In [6], the authors examined the highly symmetric class of 1-walk regular graphs, characterizing when such graphs admit unique vector colorings. We present this characterization, as well as several important consequences discussed in [5, 6]. By appealing …
Stationary Automata, Anaam Mutar Bidhan
Stationary Automata, Anaam Mutar Bidhan
Graduate Theses, Dissertations, and Problem Reports
In this dissertation, we investigate new automata, we call it stationary automata or ST-automata. This concept is based on the definition of TF-automaton by Wojciechowski [Woj2]. What is new in our approach is that we incorporate stationary subsets of limit ordinals of uncountable cofinality. The first objective of the thesis is to motivate the new construction of automata. This concept of ST-automata allows us to make a connection with infinite graph theory. Aharoni, Nash-Williams, and Shelah [AhNaSh] formulated a condition that is necessary and sufficient for a bipartite graph to have a matching. For a bipartite …