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Pages
 Title
 Bounds on the eigenvalues for certain classes of dynamic systems
 Creator
 Zeid, Mohamed Ashraf
 Date
 1982
 Collection
 Electronic Theses & Dissertations
 Title
 Independent sets in (r, s)trees
 Creator
 Cho, Junghee
 Date
 1992
 Collection
 Electronic Theses & Dissertations
 Title
 Graphs and their subdivisions
 Creator
 Stewart, Miguel James
 Date
 1972
 Collection
 Electronic Theses & Dissertations
 Title
 A combinatorial approach to knot theory : volume bounds for hyperbolic semiadequate link complements
 Creator
 Giambrone, Adam Joseph
 Date
 2014
 Collection
 Electronic Theses & Dissertations
 Description

An interesting goal in knot theory is to discover how much geometric information about a link can be carried by a representative projection diagram of that link. To this end, we show that the volumes of certain hyperbolic semiadequate links can be bounded above and below in terms of two diagrammatic quantities: the twist number and the number of special tangles in a semiadequate diagram of the link. Given this result, we then narrow our focus to families of plat closures, families of closed...
Show moreAn interesting goal in knot theory is to discover how much geometric information about a link can be carried by a representative projection diagram of that link. To this end, we show that the volumes of certain hyperbolic semiadequate links can be bounded above and below in terms of two diagrammatic quantities: the twist number and the number of special tangles in a semiadequate diagram of the link. Given this result, we then narrow our focus to families of plat closures, families of closed braids, and families of links that have both plat and closed braid aspects. By more closely studying each of these families, we can often improve the lower bounds on volume provided by the main result. Furthermore, we show that the bounds on volume can be expressed in terms of a single stable coefficient of the colored Jones polynomial. By doing this, we provide new collections of links that satisfy a Coarse Volume Conjecture. The main approach of this entire work is to use a combinatorial perspective to study the connections among knot theory, hyperbolic geometry, and graph theory.
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 Title
 The distribution of points by degree and orbit size in various species of trees
 Creator
 Bailey, Craig Kinder
 Date
 1981
 Collection
 Electronic Theses & Dissertations
 Title
 Imprimitive distancetransitive graphs
 Creator
 Furaidan, Monther Rashed
 Date
 2004
 Collection
 Electronic Theses & Dissertations
 Title
 Distancepreserving graphs
 Creator
 Nussbaum, Ronald
 Date
 2014
 Collection
 Electronic Theses & Dissertations
 Description

Let G be a simple graph on n vertices, where d_G(u,v) denotes the distance between vertices u and v in G. An induced subgraph H of G is isometric if d_H(u,v)=d_G(u,v) for all u,v in V(H). We say that G is a distancepreserving graph if G contains at least one isometric subgraph of order k for every k where 1<=k<=n.A number of sufficient conditions exist for a graph to be distancepreserving. We show that all hypercubes and graphs with delta(G)>=2n/31 are distancepreserving. Towards this end...
Show moreLet G be a simple graph on n vertices, where d_G(u,v) denotes the distance between vertices u and v in G. An induced subgraph H of G is isometric if d_H(u,v)=d_G(u,v) for all u,v in V(H). We say that G is a distancepreserving graph if G contains at least one isometric subgraph of order k for every k where 1<=k<=n.A number of sufficient conditions exist for a graph to be distancepreserving. We show that all hypercubes and graphs with delta(G)>=2n/31 are distancepreserving. Towards this end, we carefully examine the role of "forbidden" subgraphs. We discuss our observations, and provide some conjectures which we computationally verified for small values of n. We say that a distancepreserving graph is sequentially distancepreserving if each subgraph in the set of isometric subgraphs is a superset of the previous one, and consider this special case as well.There are a number of questions involving the construction of distancepreserving graphs. We show that it is always possible to add an edge to a noncomplete sequentially distancepreserving graph such that the augmented graph is still sequentially distancepreserving. We further conjecture that the same is true of all distancepreserving graphs. We discuss our observations on making nondistancepreserving graphs into distance preserving ones via adding edges. We show methods for constructing regular distancepreserving graphs, and consider constructing distancepreserving graphs for arbitrary degree sequences. As before, all conjectures here have been computationally verified for small values of n.
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 Title
 Selfcomplementary graphs : their structural properties and adjacency matrices
 Creator
 Gibbs, Richard Addison
 Date
 1970
 Collection
 Electronic Theses & Dissertations
 Title
 Enumeration of symmetries in locallyrestricted trees
 Creator
 McKeon, Kathleen A.
 Date
 1987
 Collection
 Electronic Theses & Dissertations
 Title
 Distance preserving graphs
 Creator
 Zahedi, Emad
 Date
 2017
 Collection
 Electronic Theses & Dissertations
 Description

"The computational complexity of exploring distance properties of large graphs such as realworld social networks which consist of millions of nodes is extremely expensive. Recomputing distances in subgraphs of the original graph will add to the cost. One way to avoid this is to use subgraphs where the distance between any pair of vertices is the same as in the original graph. Such a subgraph is called isometric. A connected graph is distance preserving, for which we use the abbreviation dp,...
Show more"The computational complexity of exploring distance properties of large graphs such as realworld social networks which consist of millions of nodes is extremely expensive. Recomputing distances in subgraphs of the original graph will add to the cost. One way to avoid this is to use subgraphs where the distance between any pair of vertices is the same as in the original graph. Such a subgraph is called isometric. A connected graph is distance preserving, for which we use the abbreviation dp, if it has an isometric subgraph of every order. In this framework we study dp graphs from both the structural and algorithmic perspectives. First, we study the structural nature of dp graphs. This involves classifying graphs based on the dp property and the relation between dp graphs to other graph classes. Second, we study the recognition problem of dp graphs. We intend to develop efficient algorithms for finding isometric subgraphs as well as deciding whether a graph is dp or not."Page ii.
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 Title
 Edge impact in graphs and social network matrix completion
 Creator
 Ross, Dennis
 Date
 2016
 Collection
 Electronic Theses & Dissertations
 Description

Every graph G can be associated with many wellknown invariant properties along with their corresponding values. A framework is proposed to measure the change in any particular invariant upon addition of a new edge $e$ in the resulting graph G+e. In graphs, the Pimpact of an edge e is the `magnitude' of the difference between the values of the invariant P in graphs G+e from G. Several famous invariants are explored and a proof towards optimal edge addition for distanceimpact in trees is...
Show moreEvery graph G can be associated with many wellknown invariant properties along with their corresponding values. A framework is proposed to measure the change in any particular invariant upon addition of a new edge $e$ in the resulting graph G+e. In graphs, the Pimpact of an edge e is the `magnitude' of the difference between the values of the invariant P in graphs G+e from G. Several famous invariants are explored and a proof towards optimal edge addition for distanceimpact in trees is given. A natural application to measuring the impact of edge addition to a graph is that of link prediction. An efficient algorithm for link prediction even with coldstart vertices using a subspace sharing method that decouples matrix completion and side information transduction is presented. This method is extended to predict ratings in useritem recommender systems where both may be coldstart.
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 Title
 Label propagation for classification and ranking
 Creator
 Wu, Ming
 Date
 2007
 Collection
 Electronic Theses & Dissertations
 Title
 Cluster validity and intrinsic dimensionality
 Creator
 Bailey, Thomas Anderson, Junior
 Date
 1978
 Collection
 Electronic Theses & Dissertations
 Title
 On certain pushingup problems related to vertex transitive graphs
 Creator
 Rassy, Matthias
 Date
 1998
 Collection
 Electronic Theses & Dissertations
 Title
 A graphtheoretic approach to the transport development in Iran
 Creator
 Mortezagholi, Azam
 Date
 1979
 Collection
 Electronic Theses & Dissertations
 Title
 Statistical mechanics of vertex cover
 Creator
 Fay, Charles W.
 Date
 2007
 Collection
 Electronic Theses & Dissertations
 Title
 Deletioncontraction techniques for the chromatic symmetric function of a graph
 Creator
 Gebhard, David D. (David Douglas)
 Date
 1998
 Collection
 Electronic Theses & Dissertations
 Title
 Estimation of statistical network and regionwise variable selection
 Creator
 Chakraborty, Sayan
 Date
 2016
 Collection
 Electronic Theses & Dissertations
 Description

Network models are widely used to represent relations between actors or nodes. Recent studies of the network literature and graph model revealed various characteristics of the actors and how they influenced the characteristics of neighboring actors. The first methodology is motivated by formulating a large network through the Exponential Random Graph Model and applying a Bayesian approach through the reference prior technique to control the sensitivity of the inference and to get the maximum...
Show moreNetwork models are widely used to represent relations between actors or nodes. Recent studies of the network literature and graph model revealed various characteristics of the actors and how they influenced the characteristics of neighboring actors. The first methodology is motivated by formulating a large network through the Exponential Random Graph Model and applying a Bayesian approach through the reference prior technique to control the sensitivity of the inference and to get the maximum information from the model. We consider a large Amazon product copurchasing network (customers who bought this item also bought other products), and the purpose is to show how the blending of the Exponential Random Graph Model and Bayesian Computation efficiently handles the estimation procedure and calculates the probability of certain graph structures.The second methodology we discuss is an approach to a network problem where the network adjacency structure remains unobserved, and instead we have a nodal variable that inherits a hidden network structure. The key assumption in this method is that the nodes are assumed to have a specific position in an Euclidean social space. The main analysis is based on three big U.S. auto manufacturers and their suppliers, and recent research has explored the differences of the financial markets and an emphasis has been given to reveal the strategic interactions among companies and their industry rivals and suppliers, all of which have important implications for some fundamental questions in the financial economics. Economic shocks are transmitted through the customer supplier network and the whole industry could be affected by these shocks as they can move through the links of the actors in an industry. We developed an algorithm that captures the latent linkages between firms based on sales and cost data that influence various financial decisionmaking issues and financial strategies.Finally, we extend the problem of network estimation to Bayesian variable selection whereby an observed adjacency structure between different regions has been considered. The main idea is to select relevant variables regionwise. We investigate this problem using a Bayesian approach by introducing the Bayesian Group LASSO technique with a bilevel selection that not only selects the relevant variable groups but also selects the relevant variables within that group. We use spike and slab priors, along with the Conditional Autoregressive structure among the model coefficients, which validates the spatial interaction among the covariates. Median thresholding is used instead of posterior mean to have exact zeros for the variables that are not relevant. We finally implement the problem in the auto industry data and incorporate more variables to see whether the estimated adjacency structure helps us to indicate the relevant variables over different manufacturers and suppliers.
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 Title
 The genus of cartesian products of graphs
 Creator
 White, Arthur Thomas
 Date
 1969
 Collection
 Electronic Theses & Dissertations
 Title
 Enumeration of general cubic graphs
 Creator
 Chae, GabByung
 Date
 2000
 Collection
 Electronic Theses & Dissertations