Second Hamiltonian Cycles In Claw-Free Graphs,
2015
Georgia Southern University
Second Hamiltonian Cycles In Claw-Free Graphs, Hossein Esfandiari, Colton Magnant, Pouria Salehi Nowbandegani, Shirdareh Haghighi
Theory & Applications of Graphs
Sheehan conjectured in 1975 that every Hamiltonian regular simple graph of even degree at least four contains a second Hamiltonian cycle. We prove that most claw-free Hamiltonian graphs with minimum degree at least 3 have a second Hamiltonian cycle and describe the structure of those graphs not covered by our result. By this result, we show that Sheehan’s conjecture holds for claw-free graphs whose order is not divisible by 6. In addition, we believe that the structure that we introduce can be useful for further studies on claw-free graphs.
Bounds For The Zero Forcing Number Of Graphs With Large Girth,
2015
Rice University
Bounds For The Zero Forcing Number Of Graphs With Large Girth, Randy Davila, Franklin Kenter
Theory & Applications of Graphs
The zero-forcing number, Ζ(G) is an upper bound for the maximum nullity of all symmetric matrices with a sparsity pattern described by the graph. A simple lower bound is δ ≤ Ζ(G) where δ is the minimum degree. An improvement of this bound is provided in the case that G has girth of at least 5. In particular, it is shown that 2δ − 2 ≤ Ζ(G) for graphs with girth of at least 5; this can be further improved when G has a small cut set. Lastly, a conjecture is made regarding a lower bound for Ζ(G) as a …
Dynamic Approach To K-Forcing,
2015
University of Houston - Downtown
Dynamic Approach To K-Forcing, Yair Caro, Ryan Pepper
Theory & Applications of Graphs
The k-forcing number of a graph is a generalization of the zero forcing number. In this note, we give a greedy algorithm to approximate the k-forcing number of a graph. Using this dynamic approach, we give corollaries which improve upon two theorems from a recent paper of Amos, Caro, Davila and Pepper [2], while also answering an open problem posed by Meyer [9].
Scheduling N Burgers For A K-Burger Grill: Chromatic Numbers With Restrictions,
2015
Auburn University Main Campus
Scheduling N Burgers For A K-Burger Grill: Chromatic Numbers With Restrictions, Peter Johnson, Xiaoya Zha
Theory & Applications of Graphs
The chromatic number has a well-known interpretation in the area of scheduling. If the vertices of a finite, simple graph are committees, and adjacency of two committees indicates that they must never be in session simultaneously, then the chromatic number of the graph is the smallest number of hours during which the committees/vertices of the graph may all have properly scheduled meetings of one continuous hour each. Slivnik [3] showed that the fractional chromatic number can be similarly characterized. In that characterization, the meetings are allowed to be broken into a finite number of disjoint intervals. Here we consider chromatic …
Path-Tables Of Trees: A Survey And Some New Results,
2015
University of Malta
Path-Tables Of Trees: A Survey And Some New Results, Kevin Asciak
Theory & Applications of Graphs
The (vertex) path-table of a tree Τ contains quantitative information about the paths in Τ. The entry (i,j) of this table gives the number of paths of length j passing through vertex vi. The path-table is a slight variation of the notion of path layer matrix. In this survey we review some work done on the vertex path-table of a tree and also introduce the edge path-table. We show that in general, any type of path-table of a tree Τ does not determine Τ uniquely. We shall show that in trees, the number of paths passing through …
Connection And Separation In Hypergraphs,
2015
Illinois State University
Connection And Separation In Hypergraphs, Mohammad A. Bahmanian, Mateja Sajna
Theory & Applications of Graphs
In this paper we study various fundamental connectivity properties of hypergraphs from a graph-theoretic perspective, with the emphasis on cut edges, cut vertices, and blocks. We prove a number of new results involving these concepts. In particular, we describe the exact relationship between the block decomposition of a hypergraph and the block decomposition of its incidence graph.
Modeling Human Gaming Playing Behavior And Reward/Penalty Mechanism Using Discrete Event Simulation (Des),
2015
Embry-Riddle Aeronautical University
Modeling Human Gaming Playing Behavior And Reward/Penalty Mechanism Using Discrete Event Simulation (Des), Christina M. Frederick, Michael Fitzgerald, Dahai Liu, Yolanda Ortiz, Christopher Via, Shawn Doherty, Jason P. Kring
Publications
Humans are remarkably complex and unpredictable; however, while predicting human behavior can be problematic, there are methods such as modeling and simulation that can be used to predict probable futures of human decisions. The present study analyzes the possibility of replacing human subjects with data resulting from pure models. Decisions made by college students in a multi-level mystery-solving game under 3 different gaming conditions are compared with the data collected from a predictive sequential Markov-Decision Process model. In addition, differences in participants’ data influenced by the three different conditions (additive, subtractive, control) were analyzed. The test results strongly suggest that …
Community Detection Detailed For Online Social Networks,
2015
Wilfrid Laurier University
Community Detection Detailed For Online Social Networks, Christopher J. Hogan
Theses and Dissertations (Comprehensive)
Ever since the internet became publicly available it has allowed users to interact with each other across virtual networks. With this large amounts of data being collected the clustering of this information has become an even more powerful tool for recognize patterns and trends in a network. In this research we look build a model for Community Detection in these online social networks. We combine the ideas from both discrete mathematics and sociology, to build an algorithm with the specific intent on discovering communities that exist in an online social network. We present many of the sociology theories behind the …
Multidimensional Mod Planes,
2015
University of New Mexico
Multidimensional Mod Planes, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Branch Mathematics and Statistics Faculty and Staff Publications
In this book authors name the interval [0, m); 2 ≤ m ≤ ∞ as mod interval. We have studied several properties about them but only here on wards in this book and forthcoming books the interval [0, m) will be termed as the mod real interval, [0, m)I as mod neutrosophic interval, [0,m)g; g2 = 0 as mod dual number interval, [0, m)h; h2 = h as mod special dual like number interval and [0, m)k, k2 = (m − 1) k as mod special quasi dual number interval. However there is only one real interval (∞, ∞) but …
Neutrosophic Graphs: A New Dimension To Graph Theory,
2015
University of New Mexico
Neutrosophic Graphs: A New Dimension To Graph Theory, Florentin Smarandache, Wb. Vasantha Kandasamy, K. Ilanthenral
Branch Mathematics and Statistics Faculty and Staff Publications
In this book authors for the first time have made a through study of neutrosophic graphs. This study reveals that these neutrosophic graphs give a new dimension to graph theory. The important feature of this book is it contains over 200 neutrosophic graphs to provide better understanding of this concepts. Further these graphs happen to behave in a unique way inmost cases, for even the edge colouring problem is different from the classical one. Several directions and dimensions in graph theory are obtained from this study. Finally certainly these new notions of neutrosophic graphs in general and in particular the …
Special Type Of Topological Spaces Using [0, N),
2015
University of New Mexico
Special Type Of Topological Spaces Using [0, N), Florentin Smarandache, W.B Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
In this book authors for the first time introduce the notion of special type of topological spaces using the interval [0, n). They are very different from the usual topological spaces. Algebraic structure using the interval [0, n) have been systemically dealt by the authors. Now using those algebraic structures in this book authors introduce the notion of special type of topological spaces. Using the super subset interval semigroup special type of super interval topological spaces are built. Several interesting results in this direction are obtained. Next six types of topological spaces using subset interval pseudo ring semiring of type …
Mod Functions: A New Approach To Function Theory,
2015
University of New Mexico
Mod Functions: A New Approach To Function Theory, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Branch Mathematics and Statistics Faculty and Staff Publications
In this book the notion of MOD functions are defined on MOD planes. This new concept of MOD functions behaves in a very different way. Even very simple functions like y = nx has several zeros in MOD planes where as they are nice single line graphs with only (0, 0) as the only zero. Further polynomials in MOD planes do not in general follows the usual or classical laws of differentiation or integration. Even finding roots of MOD polynomials happens to be very difficult as they do not follow the fundamental theorem of algebra, viz a nth degree polynomial …
Mod Planes: A New Dimension To Modulo Theory,
2015
University of New Mexico
Mod Planes: A New Dimension To Modulo Theory, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Branch Mathematics and Statistics Faculty and Staff Publications
In this book for the first time authors study mod planes using modulo intervals [0, m); 2 ≤ m ≤ ∞. These planes unlike the real plane have only one quadrant so the study is carried out in a compact space but infinite in dimension. We have given seven mod planes viz real mod planes (mod real plane) finite complex mod plane, neutrosophic mod plane, fuzzy mod plane, (or mod fuzzy plane), mod dual number plane, mod special dual like number plane and mod special quasi dual number plane. These mod planes unlike real plane or complex plane or neutrosophic …
Mod Pseudo Linear Algebras,
2015
University of New Mexico
Mod Pseudo Linear Algebras, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral
Branch Mathematics and Statistics Faculty and Staff Publications
In this book authors for the first time elaborately study the notion of MOD vector spaces and MOD pseudo linear algebras. This study is new, innovative and leaves several open conjectures. In the first place as distributive law is not true we can define only MOD pseudo linear algebras. Secondly most of the classical theorems true in case of linear algebras are not true in case of MOD pseudo linear algebras. Finding even eigen values and eigen vectors happens to be a challenging problem. Further the notion of multidimensional MOD pseudo linear algebras are defined using the notion of MOD …
Fuzzy Abel Grassmann Groupoids,
2015
University of New Mexico
Fuzzy Abel Grassmann Groupoids, Florentin Smarandache, Madad Khan, Tariq Aziz
Branch Mathematics and Statistics Faculty and Staff Publications
Usually the models of real world problems in almost all disciplines like engineering, medical sciences, mathematics, physics, computer science, management sciences, operations research and articial intelligence are mostly full of complexities and consist of several types of uncertainties while dealing them in several occasion. To overcome these di¢ culties of uncertainties, many theories have been developed such as rough sets theory, probability theory, fuzzy sets theory, theory of vague sets, theory of soft ideals and the theory of intuitionistic fuzzy sets, theory of neutrosophic sets, Dezert-Smarandache Theory (DSmT), etc. Zadeh introduced the degree of membership/truth (t) in 1965 and dened …
Theory Of Abel Grassmann's Groupoids,
2015
University of New Mexico
Theory Of Abel Grassmann's Groupoids, Florentin Smarandache, Madad Khan
Branch Mathematics and Statistics Faculty and Staff Publications
It is common knowledge that common models with their limited boundaries of truth and falsehood are not su¢ cient to detect the reality so there is a need to discover other systems which are able to address the daily life problems. In every branch of science problems arise which abound with uncertainties and impaction. Some of these problems are related to human life, some others are subjective while others are objective and classical methods are not su¢ cient to solve such problems because they can not handle various ambiguities involved. To overcome this problem, Zadeh [67] introduced the concept of …
Modeling The Progress And Retention Of International Students Using Markov Chains,
2015
University of Akron Main Campus
Modeling The Progress And Retention Of International Students Using Markov Chains, Lucas Gagne
Williams Honors College, Honors Research Projects
International students are a small and diverse student population present in any sizable American university. One of the greatest obstacles in their path is the acquisition of the English language. English for Academic Purposes (EAP) programs, such as the English Language Institute (ELI) at the University of Akron, attempt to address this problem. By studying how this student population progresses in their academic studies, EAP programs and their associated universities can make well-informed decisions on how best to serve their English Language Learners. One way to study International students is through the use of a Markov model based on university …
Some Properties Of The Exchange Operator With Respect To Structured Matrices Defined By Indefinite Scalar Product Spaces,
2015
Ateneo de Manila University
Some Properties Of The Exchange Operator With Respect To Structured Matrices Defined By Indefinite Scalar Product Spaces, Hanz Martin C. Cheng, Roden Jason David
Mathematics Faculty Publications
The properties of the exchange operator on some types of matrices are explored in this paper. In particular, the properties of exc(A,p,q), where A is a given structured matrix of size (p+q)Ã(p+q) and exc : M ÃNÃN â M is the exchange operator are studied. This paper is a generalization of one of the results in [N.J. Higham. J-orthogonal matrices: Properties and generation. SIAM Review, 45:504â519, 2003.].
Inner Product Spaces And Krein Spaces In The Quaternionic Setting,
2015
Chapman University
Inner Product Spaces And Krein Spaces In The Quaternionic Setting, Daniel Alpay, Fabrizio Colombo, Irene Sabadini
Mathematics, Physics, and Computer Science Faculty Articles and Research
In this paper we provide a study of quaternionic inner product spaces. This includes ortho-complemented subspaces, fundamental decompositions as well as a number of results of topological nature. Our main purpose is to show that a closed uniformly positive subspace in a quaternionic Krein space is ortho-complemented, and this leads to our choice of the results presented in the paper.
I Don't Play Chess: A Study Of Chess Piece Generating Polynomials,
2015
The College of Wooster
I Don't Play Chess: A Study Of Chess Piece Generating Polynomials, Stephen R. Skoch
Senior Independent Study Theses
This independent study examines counting problems of non-attacking rook, and non-attacking bishop placements. We examine boards for rook and bishop placement with restricted positions and varied dimensions. In this investigation, we discuss the general formula of a generating function for unrestricted, square bishop boards that relies on the Stirling numbers of the second kind. We discuss the maximum number of bishops we can place on a rectangular board, as well as a brief investigation of non-attacking rook placements on three-dimensional boards, drawing a connection to latin squares.
