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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 semi-adequate 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 semi-adequate links can be bounded above and below in terms of two diagrammatic quantities: the twist number and the number of special tangles in a semi-adequate 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 semi-adequate links can be bounded above and below in terms of two diagrammatic quantities: the twist number and the number of special tangles in a semi-adequate 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 distance-transitive graphs
- Creator
- Furaidan, Monther Rashed
- Date
- 2004
- Collection
- Electronic Theses & Dissertations
- Title
- Distance-preserving graphs
- Creator
- Nussbaum, Ronald
- Date
- 2014
- Collection
- Electronic Theses & Dissertations
- Description
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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 distance-preserving 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 distance-preserving. We show that all hypercubes and graphs with delta(G)>=2n/3-1 are distance-preserving. 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 distance-preserving 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 distance-preserving. We show that all hypercubes and graphs with delta(G)>=2n/3-1 are distance-preserving. 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 distance-preserving graph is sequentially distance-preserving 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 distance-preserving graphs. We show that it is always possible to add an edge to a non-complete sequentially distance-preserving graph such that the augmented graph is still sequentially distance-preserving. We further conjecture that the same is true of all distance-preserving graphs. We discuss our observations on making non-distance-preserving graphs into distance preserving ones via adding edges. We show methods for constructing regular distance-preserving graphs, and consider constructing distance-preserving graphs for arbitrary degree sequences. As before, all conjectures here have been computationally verified for small values of n.
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- Title
- Self-complementary graphs : their structural properties and adjacency matrices
- Creator
- Gibbs, Richard Addison
- Date
- 1970
- Collection
- Electronic Theses & Dissertations
- Title
- Enumeration of symmetries in locally-restricted 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 real-world 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 real-world 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
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Every graph G can be associated with many well-known 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 P-impact 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 distance-impact in trees is...
Show moreEvery graph G can be associated with many well-known 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 P-impact 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 distance-impact 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 cold-start vertices using a subspace sharing method that decouples matrix completion and side information transduction is presented. This method is extended to predict ratings in user-item recommender systems where both may be cold-start.
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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 pushing-up problems related to vertex transitive graphs
- Creator
- Rassy, Matthias
- Date
- 1998
- Collection
- Electronic Theses & Dissertations
- Title
- A graph-theoretic 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
- Deletion-contraction 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 region-wise 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 co-purchasing 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 decision-making 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 region-wise. We investigate this problem using a Bayesian approach by introducing the Bayesian Group LASSO technique with a bi-level 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, Gab-Byung
- Date
- 2000
- Collection
- Electronic Theses & Dissertations