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Articles 1 - 30 of 144
Full-Text Articles in Applied Mathematics
Line Graphs Of Directed Graphs I, Vaidy Sivaraman, Daniel Slilaty
Line Graphs Of Directed Graphs I, Vaidy Sivaraman, Daniel Slilaty
Mathematics and Statistics Faculty Publications
We determine the forbidden induced subgraphs for the intersection of the classes of chordal bipartite graphs and line graphs of acyclic directed graphs. This is a first step towards finding the forbidden induced subgraphs for the class of line graphs of directed graphs.
On Colorings And Orientations Of Signed Graphs, Daniel Slilaty
On Colorings And Orientations Of Signed Graphs, Daniel Slilaty
Mathematics and Statistics Faculty Publications
A classical theorem independently due to Gallai and Roy states that a graph G has a proper k-coloring if and only if G has an orientation without coherent paths of length k. An analogue of this result for signed graphs is proved in this article.
Graphs Without A 2c3-Minor And Bicircular Matroids Without A U3,6-Minor, Daniel Slilaty
Graphs Without A 2c3-Minor And Bicircular Matroids Without A U3,6-Minor, Daniel Slilaty
Mathematics and Statistics Faculty Publications
In this note we characterize all graphs without a 2C3-minor. A consequence of this result is a characterization of the bicircular matroids with no U3,6-minor.
Odd Solutions To Systems Of Inequalities Coming From Regular Chain Groups, Daniel Slilaty
Odd Solutions To Systems Of Inequalities Coming From Regular Chain Groups, Daniel Slilaty
Mathematics and Statistics Faculty Publications
Hoffman’s theorem on feasible circulations and Ghouila-Houry’s theorem on feasible tensions are classical results of graph theory. Camion generalized these results to systems of inequalities over regular chain groups. An analogue of Camion’s result is proved in which solutions can be forced to be odd valued. The obtained result also generalizes the results of Pretzel and Youngs as well as Slilaty. It is also shown how Ghouila-Houry’s result can be used to give a new proof of the graph- coloring theorem of Minty and Vitaver.
Hamilton Cycles In Bidirected Complete Graphs, Arthur Busch, Mohammed A. Mutar, Daniel Slilaty
Hamilton Cycles In Bidirected Complete Graphs, Arthur Busch, Mohammed A. Mutar, Daniel Slilaty
Mathematics and Statistics Faculty Publications
Zaslavsky observed that the topics of directed cycles in directed graphs and alternating cycles in edge 2-colored graphs have a common generalization in the study of coherent cycles in bidirected graphs. There are classical theorems by Camion, Harary and Moser, Häggkvist and Manoussakis, and Saad which relate strong connectivity and Hamiltonicity in directed "complete" graphs and edge 2-colored "complete" graphs. We prove two analogues to these theorems for bidirected "complete" signed graphs.
Numerical Solutions To The Robin Inverse Problem With Nonnegativity Constraints, Weifu Fang, Fu-Rong Lin
Numerical Solutions To The Robin Inverse Problem With Nonnegativity Constraints, Weifu Fang, Fu-Rong Lin
Mathematics and Statistics Faculty Publications
We present iterative numerical methods for solving the inverse problem of recovering the nonnegative Robin coefficient from partial boundary measurement of the solution to the Laplace equation. Based on the boundary integral equation formulation of the problem, nonnegativity constraints in the form of a penalty term are incorporated conveniently into least-squares iteration schemes for solving the inverse problem. Numerical implementation and examples are presented to illustrate the effectiveness of this strategy in improving recovery results.
Characterization Of A Family Of Rotationally Symmetric Spherical Quadrangulations, Lowell Abrams, Daniel Slilaty
Characterization Of A Family Of Rotationally Symmetric Spherical Quadrangulations, Lowell Abrams, Daniel Slilaty
Mathematics and Statistics Faculty Publications
A spherical quadrangulation is an embedding of a graph G in the sphere in which each facial boundary walk has length four. Vertices that are not of degree four in G are called curvature vertices. In this paper we classify all spherical quadrangulations with n-fold rotational symmetry (n ≥ 3) that have minimum degree 3 and the least possible number of curvature vertices, and describe all such spherical quadrangulations in terms of nets of quadrilaterals. The description reveals that such rotationally symmetric quadrangulations necessarily also have a pole-exchanging symmetry.
A Unified Approach For Constructing Confidence Intervals And Hypothesis Tests Using H-Function, Weizhen Wang
A Unified Approach For Constructing Confidence Intervals And Hypothesis Tests Using H-Function, Weizhen Wang
Mathematics and Statistics Faculty Publications
We introduce a general method, named the h-function method, to unify the constructions of level-a exact test and 1-a exact confidence interval. Using this method, any confidence interval is improved as follows: i) an approximate interval, including a point estimator, is modified to an exact interval; ii) an exact interval is refined to be an interval that is a subset of the previous one. Two real datasets are used to illustrate the method.
Coloring Permutation-Gain Graphs, Daniel Slilaty
Coloring Permutation-Gain Graphs, Daniel Slilaty
Mathematics and Statistics Faculty Publications
Correspondence colorings of graphs were introduced in 2018by Dvoˇr ́ak and Postle as a generalization of list colorings of graphswhich generalizes ordinary graph coloring. Kim and Ozeki observed thatcorrespondence colorings generalize various notions of signed-graph col-orings which again generalizes ordinary graph colorings. In this notewe state how correspondence colorings generalize Zaslavsky’s notionof gain-graph colorings and then formulate a new coloring theory ofpermutation-gain graphs that sits between gain-graph coloring and cor-respondence colorings. Like Zaslavsky’s gain-graph coloring, our newnotion of coloring permutation-gain graphs has well defined chromaticpolynomials and lifts to colorings of the regular covering graph of apermutation-gain graph
The Family Of Bicircular Matroids Closed Under Duality, Vaidy Sivaraman, Daniel Slilaty
The Family Of Bicircular Matroids Closed Under Duality, Vaidy Sivaraman, Daniel Slilaty
Mathematics and Statistics Faculty Publications
We characterize the 3-connected members of the intersection of the class of bicircular and cobi- circular matroids. Aside from some exceptional matroids with rank and corank at most 5, this class consists of just the free swirls and their minors.
Describing Quasi-Graphic Matroids, Nathan Bowler, Daryl Funk, Dan Slilaty
Describing Quasi-Graphic Matroids, Nathan Bowler, Daryl Funk, Dan Slilaty
Mathematics and Statistics Faculty Publications
The class of quasi-graphic matroids recently introduced by Geelen, Gerards, and Whittle generalises each of the classes of frame matroids and liftedgraphic matroids introduced earlier by Zaslavsky. For each biased graph (G, B) Zaslavsky defined a unique lift matroid L(G, B) and a unique frame matroid F(G, B), each on ground set E(G). We show that in general there may be many quasi-graphic matroids on E(G) and describe them all: for each graph G and partition (B, L, F) of its cycles such that B satisfies the theta property and each cycle in L meets each cycle in F, there …
The Graphs That Have Antivoltages Using Groups Of Small Order, Vaidy Sivaraman, Dan Slilaty
The Graphs That Have Antivoltages Using Groups Of Small Order, Vaidy Sivaraman, Dan Slilaty
Mathematics and Statistics Faculty Publications
Given a group Γ of order at most six, we characterize the graphs that have Γ-antivoltages and also determine the list of minor-minimal graphs that have no Γ-antivoltage. Our characterizations yield polynomial-time recognition algorithms for such graphs.
Bounding And Stabilizing Realizations Of Biased Graphs With A Fixed Group, Nancy Ann Neudauer, Dan Slilaty
Bounding And Stabilizing Realizations Of Biased Graphs With A Fixed Group, Nancy Ann Neudauer, Dan Slilaty
Mathematics and Statistics Faculty Publications
Given a group Γ and a biased graph (G, B), we define a what is meant by a Γ-realization of (G, B) and a notion of equivalence of Γ-realizations. We prove that for a finite group Γ and t ≥ 3, that there are numbers n(Γ) and n(Γ, t) such that the number of Γ-realizations of a vertically 3-connected biased graph is at most n(Γ) and that the number of Γ-realizations of a nonseparable biased graph without a (2Ct , ∅)-minor is at most n(Γ, t). Other results pertaining to contrabalanced biased graphs are presented as well as an analogue …
Flexibility Of Projective-Planar Embeddings, John Maharry, Neil Robertson, Vaidy Sivaraman, Dan Slilaty
Flexibility Of Projective-Planar Embeddings, John Maharry, Neil Robertson, Vaidy Sivaraman, Dan Slilaty
Mathematics and Statistics Faculty Publications
Given two embeddings σ1 and σ2 of a labeled nonplanar graph in the projective plane, we give a collection of maneuvers on projective-planar embeddings that can be used to take σ1 to σ2
Projective-Planar Graphs With No K3,4-Minor. Ii., John Maharry, Dan Slilaty
Projective-Planar Graphs With No K3,4-Minor. Ii., John Maharry, Dan Slilaty
Mathematics and Statistics Faculty Publications
The authors previously published an iterative process to generate a class of projectiveplanar K3,4-free graphs called ‘patch graphs’. They also showed that any simple, almost 4-connected, nonplanar, and projective-planar graph that is K3,4-free is a subgraph of a patch graph. In this paper, we describe a simpler and more natural class of cubic K3,4- free projective-planar graphs which we call M¨obius hyperladders. Furthermore, every simple, almost 4-connected, nonplanar, and projective-planar graph that is K3,4-free is a minor of a M¨obius hyperladder. As applications of these structures we determine the page number of patch graphs and of M¨obius hyperladders.
Wright State University Math And Statistics Department History, Joanne Dombrowski, David Miller
Wright State University Math And Statistics Department History, Joanne Dombrowski, David Miller
Mathematics and Statistics Faculty Publications
No abstract provided.
The Minimal Zn-Symmetric Graphs That Are Not Zn-Spherical, Lowell Abrams, Dan Slilaty
The Minimal Zn-Symmetric Graphs That Are Not Zn-Spherical, Lowell Abrams, Dan Slilaty
Mathematics and Statistics Faculty Publications
Given a graph G equipped with faithful and fixed-point-free Γ-action (Γ a finite group) we define an orbit minor H of G to be a minor of G for which the deletion and contraction sets are closed under the Γ-action. The orbit minor H inherits a Γ-symmetry from G, and when the contraction set is acyclic the action inherited by H remains faithful and fixed-point free. When G embeds in the sphere and the Γ-action on G extends to a Γ-action on the entire sphere, we say that G is Γ-spherical. In this paper we determine for every odd value …
Unavoidable Minors Of Large 4-Connected Bicircular Matroids, Deborah Chun, Tyler Moss, Dan Slilaty, Xiangqian Zhou
Unavoidable Minors Of Large 4-Connected Bicircular Matroids, Deborah Chun, Tyler Moss, Dan Slilaty, Xiangqian Zhou
Mathematics and Statistics Faculty Publications
It is known that any 3-connected matroid that is large enough is certain to contain a minor of a given size belonging to one of a few special classes of matroids. This paper proves a similar unavoidable minor result for large 4-connected bicircular matroids. The main result follows from establishing the list of unavoidable minors of large 4-biconnected graphs, which are the graphs representing the 4-connected bicircular matroids. This paper also gives similar results for internally 4-connected and vertically 4-connected bicircular matroids.
Multi-Peak Solutions To Two Types Of Free Boundary Problems, Yi Li, Shuangjie Peng
Multi-Peak Solutions To Two Types Of Free Boundary Problems, Yi Li, Shuangjie Peng
Mathematics and Statistics Faculty Publications
We consider the existence of multi-peak solutions to two types of free boundary problems arising in confined plasma and steady vortex pair under conditions on the nonlinearity we believe to be almost optimal. Our results show that the “core” of the solution has multiple connected components, whose boundary called free boundary of the problems consists approximately of spheres which shrink to distinct single points as the parameter tends to zero.
Some Minor-Closed Classes Of Signed Graphs, Dan Slilaty, Xiangqian Zhou
Some Minor-Closed Classes Of Signed Graphs, Dan Slilaty, Xiangqian Zhou
Mathematics and Statistics Faculty Publications
We define four minor-closed classes of signed graphs in terms of embeddability in the annulus, projective plane, torus, and Klein bottle. We give the full list of 20 excluded minors for the smallest class and make a conjecture about the largest class.
Group Developed Weighing Matrices, K. T. Arasu, Jeffrey R. Hollon
Group Developed Weighing Matrices, K. T. Arasu, Jeffrey R. Hollon
Mathematics and Statistics Faculty Publications
A weighing matrix is a square matrix whose entries are 1, 0 or −1, such that the matrix times its transpose is some integer multiple of the identity matrix. We examine the case where these matrices are said to be devel- oped by an abelian group. Through a combination of extending previous results and by giving explicit constructions we will answer the question of existence for 318 such matrices of order and weight both below 100. At the end, we are left with 98 open cases out of a possible 1,022. Further, some of the new results provide insight into …
Translation Representations And Scattering By Two Intervals, Palle Jorgensen, Steen Pedersen, Feng Tian
Translation Representations And Scattering By Two Intervals, Palle Jorgensen, Steen Pedersen, Feng Tian
Mathematics and Statistics Faculty Publications
Studying unitary one-parameter groups in Hilbert space (U(t), H), we show that a model for obstacle scattering can be built, up to unitary equivalence, with the use of translation representations for L2-functions in the complement of two finite and disjoint intervals. The model encompasses a family of systems (U(t), H). For each, we obtain a detailed spectral representation, and we compute the scattering operator and scattering matrix. We illustrate our results in the Lax-Phillips model where (U(t), H) represents an acoustic wave equation …
The Constructions Of Almost Binary Sequence Pairs And Binary Sequence Pairs With Three-Level Autocorrelation, Xiuping Peng, Chengqian Xu, Guang Li, Krishnasamy T. Arasu
The Constructions Of Almost Binary Sequence Pairs And Binary Sequence Pairs With Three-Level Autocorrelation, Xiuping Peng, Chengqian Xu, Guang Li, Krishnasamy T. Arasu
Mathematics and Statistics Faculty Publications
In this letter, a new class of almost binary sequence pairs with a single zero element and three autocorrelation values is presented. The new almost binary sequence pairs are based on cyclic difference sets and difference set pairs. By applying the method to the binary sequence pairs, new binary sequence pairs with three-level autocorrelation are constructed. It is shown that new sequence pairs from our constructions are balanced or almost balanced and have optimal three-level autocorrelation when the characteristic sequences or sequence pairs of difference sets or difference set pairs are balanced or almost balanced and have optimal autocorrelations.
Multiple Solutions For An Elliptic Problem Related To Vortex Pairs, Yi Li, Shuangjie Peng
Multiple Solutions For An Elliptic Problem Related To Vortex Pairs, Yi Li, Shuangjie Peng
Mathematics and Statistics Faculty Publications
Let Ω be a bounded domain in RN (N⩾2), φ a harmonic function in Ω¯. In this paper we study the existence of solutions to the following problem arising in the study of vortex pairs(Pλ){−Δu=λ(u−φ)+p−1,x∈Ω,u=0,x∈∂Ω. The set Ωp={x∈Ω,u(x)>φ} is called “vortex core”. Existence of solutions whose “vortex core” consists of one component and asymptotic behavior of “vortex core” were studied by many authors for large λ recently. Under the condition that φ has k strictly local minimum points on the boundary ∂Ω, we obtain in this paper that for λ large enough, (Pλ) has a solution with “vortex core” …
Quantitative Interpretation Of A Genetic Model Of Carcinogenesis Using Computer Simulations, Donghai Dai, Brandon Beck, Xiaofang Wang, Cory Howk, Yi Li
Quantitative Interpretation Of A Genetic Model Of Carcinogenesis Using Computer Simulations, Donghai Dai, Brandon Beck, Xiaofang Wang, Cory Howk, Yi Li
Mathematics and Statistics Faculty Publications
The genetic model of tumorigenesis by Vogelstein et al. (V theory) and the molecular definition of cancer hallmarks by Hanahan and Weinberg (W theory) represent two of the most comprehensive and systemic understandings of cancer. Here, we develop a mathematical model that quantitatively interprets these seminal cancer theories, starting from a set of equations describing the short life cycle of an individual cell in uterine epithelium during tissue regeneration. The process of malignant transformation of an individual cell is followed and the tissue (or tumor) is described as a composite of individual cells in order to quantitatively account for intra-tumor …
Projective-Planar Graphs With No K3,4-Minor, John Maharry, Dan Slilaty
Projective-Planar Graphs With No K3,4-Minor, John Maharry, Dan Slilaty
Mathematics and Statistics Faculty Publications
An exact structure is described to classify the projective‐planar graphs that do not contain a K3, 4‐minor.
The Positive Solutions Of The Matukuma Equation And The Problem Of Finite Radius And Finite Mass, Jurgen Batt, Yi Li
The Positive Solutions Of The Matukuma Equation And The Problem Of Finite Radius And Finite Mass, Jurgen Batt, Yi Li
Mathematics and Statistics Faculty Publications
This work is an extensive study of the 3 different types of positive solutions of the Matukuma equation 1r2(r2ϕ′)′=−rλ−2(1+r2)λ/2ϕp,p>1,λ>0 : the E-solutions (regular at r = 0), the M-solutions (singular at r = 0) and the F-solutions (whose existence begins away from r = 0). An essential tool is a transformation of the equation into a 2-dimensional asymptotically autonomous system, whose limit sets (by a theorem of H. R. Thieme) are the limit sets of Emden–Fowler systems, and serve as a characterization of the different solutions. The emphasis lies on the study of the M …
On Circulant And Two-Circulant Weighing Matrices, K. T. Arasu, I. S. Kotsireast, C. Koukouvinos, Jennifer Seberry
On Circulant And Two-Circulant Weighing Matrices, K. T. Arasu, I. S. Kotsireast, C. Koukouvinos, Jennifer Seberry
Mathematics and Statistics Faculty Publications
We employ theoretical and computational techniques to construct new weighing matrices constructed from two circulants. In particular, we con- struct W (148, 144), W (152, 144), W (156, 144) which are listed as open in the second edition of the Handbook of Combinatorial Designs. We also fill a missing entry in Strassler’s table with answer “YES”, by constructing a circulant weighing matrix of order 142 with weight 100.
On Construction Of The Smallest One-Sided Confidence Interval For The Difference Of Two Proportions, Weizhen Wang
On Construction Of The Smallest One-Sided Confidence Interval For The Difference Of Two Proportions, Weizhen Wang
Mathematics and Statistics Faculty Publications
For my class of one-sided 1 - α confidence intervals with a certain monotonicity ordering on the random confidence limit, the smallest interval, in the sense of the set inclusion for the difference of two proportions of two independent binomial random variables, is constructed based on a direct analysis of coverage probability function. A special ordering on the confidence limit is developed and the corresponding smallest confidence interval is derived. This interval is then applied to identify the minimum effective dose (MED) for binary data in dose-response studies, and a multiple test procedure that controls the familywise error rate at …
Integer Functions On The Cycle Space And Edges Of A Graph, Dan Slilaty
Integer Functions On The Cycle Space And Edges Of A Graph, Dan Slilaty
Mathematics and Statistics Faculty Publications
A directed graph has a natural Z-module homomorphism from the underlying graph’s cycle space to Z where the image of an oriented cycle is the number of forward edges minus the number of backward edges. Such a homomorphism preserves the parity of the length of a cycle and the image of a cycle is bounded by the length of that cycle. Pretzel and Youngs (SIAM J. Discrete Math. 3(4):544–553, 1990) showed that any Z-module homomorphism of a graph’s cycle space to Z that satisfies these two properties for all cycles must be such a map induced from an edge direction …