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Full-Text Articles in Mathematics
Computing Well-Structured Subgraphs In Geometric Intersection Graphs., Satyabrata Jana Dr.
Computing Well-Structured Subgraphs In Geometric Intersection Graphs., Satyabrata Jana Dr.
Doctoral Theses
For a set of geometric objects, the associative geometric intersection graph is the graph with a vertex for each object and an edge between two vertices if and only if the corresponding objects intersect. Geometric intersection graphs are very important due to their theoretical properties and applicability. Based on the different geometric objects, several types of geometric intersection graphs are defined. Given a graph G, an induced (either vertex or edge) subgraph H ⊆ G is said to be an well-structured subgraph if H satisfies certain properties among the vertices in H. This thesis studies some well-structured subgraphs finding problems …
On The Approximability Of Linear Ordering And Related Np-Optimization Problems., Sounaka Mishra Dr.
On The Approximability Of Linear Ordering And Related Np-Optimization Problems., Sounaka Mishra Dr.
Doctoral Theses
We investigate approximability of both maximum and minimum linear ordering problems (MAX-LOP and MIN-LOP) and several related problems such as the well known feedback set problems, acyclie subdigraph problem and several others and their variants.We show that both MAX-LOP and MIN-LOP are strongly NP-complete, and MIN- LOP, MIN-QAP(S) (a special case of minimum quadratic assignment problem) and MIN-W-FAS are equivalent with respect to strict-reduction. The strict-equivalence is also established among these problems as well as MIN-W-FVS, with weights on arcs/vertices bounded by a polynomial, and the unweighted versions of the feedback set. problems. We also show that MAX-LOP is strict-equivalent …
Perturbed Laplacian Matrix And The Structure Of A Graph., Sukanta Pati Dr.
Perturbed Laplacian Matrix And The Structure Of A Graph., Sukanta Pati Dr.
Doctoral Theses
Laplacian matrices Let G be a connected simple graph with vertex set V = {1,2,.,n), edge set E and let each edge be associated with a positive number, the weight of the edge. The above graph is called a weighted graph. An unweighted graph is just a weighted graph with each of the edges bearing weight 1. All the graphs considered are weighted and simple, unless specified otherwise; all the matrices considered are real. The adjacency matrix A(G) related to this graph is defined as A(G) = (aij), whereaij, if (i, j] € E and the weight of the edge …
On The Geometrisability Of Some Strongly Regular Graphs Related To Polar Spaces., Pratima Panigraphi Dr.
On The Geometrisability Of Some Strongly Regular Graphs Related To Polar Spaces., Pratima Panigraphi Dr.
Doctoral Theses
GraphsA graph G = (VE) consists of a finite set V and a subset E of ). (Here () denotes the set of all 2-subsets of V.) Elements of Vare called the vertices and the elements of E are called the edges of the graph. So Vis the vertex set and E is the edge set of the graph G. Two vertices a, y are said to be adjacent if the pair {a, y} is an edge; otherwise they are non-adjacent. If two vertices are adjacent then each is called a neighbour of the other vertex.Sometimes the edges of a …
New Topologies And Parallel Algorithms For Static Interconnection Networks., Srabani Sen Gupta Dr.
New Topologies And Parallel Algorithms For Static Interconnection Networks., Srabani Sen Gupta Dr.
Doctoral Theses
Many real-life applications in the areas of signal processing, image processing, etc., require a large amount of fast computations to be performed. Although high speed powerful processors are currently available due to the phenomenal advances in VLSI technology, the increasing demand for massive real-time computations can not be met just by a uniprocessor system. One way of achieving the goal of fast computation is through parallel processing. In parallel processing, a problem is broken into several subproblems, which are distributed among different processors so that each of the processors can perform its task simultaneously. Main areas of recent research in …
Design,Analysis And Routing In Static Interconnection Networks., Rajib Kumar Das Dr.
Design,Analysis And Routing In Static Interconnection Networks., Rajib Kumar Das Dr.
Doctoral Theses
Many real-life applications such as image processing, weather forecasting, digital signal processing, etc., require large amount of computations. By distributing the task among several processors, one can appreciably reduce the computation time. To solve complex problems, several computer architectures using multiple processors have been introduced. Recent developments in IC technology have made it economically feasible to construct multiple processor systems consisting of hundreds or thousands of processors.There are two types of multiprocessor systems (PS87). One is tightly coupled, where the processors share a common clock and/or memory. The other is loosely coupled, where each processor runs independently with a local …
Computer Squares And Principal Graphs Of Subfactors., Uma Krishnan Dr.
Computer Squares And Principal Graphs Of Subfactors., Uma Krishnan Dr.
Doctoral Theses
This thosin in devoted to the study of aome probloms related to the inclusion of a pair of (usually hyperfinite) Ili factors R. Specifically, the following and the relation between them are studied:(a) pairs of graphs which can occur as principal grapha for NC M;(b) construction of commuting squares starting with a pair of finite graphs;(c) computation of the higher relative commutants of sublactorn con- structed from specific commuting squares.The first chapter is introductory in nature and is included for the sake of comploteness and convenience of reference. It contains a rather perfunctory description of the basic construction for a …
Hypergroup Graphs And Subfactors., A. K. Vijayarajan Dr.
Hypergroup Graphs And Subfactors., A. K. Vijayarajan Dr.
Doctoral Theses
The main theme of this t hesis is hypergroups. In this thesis the the- ory of hypergroups is applied to study the relation between certain graphs and subfactors of II, factors in the context of principal graphs associated with the inclusions of II, factors. More general classes of hypergroups are iutroduced, new examples of hypergroups associated to certain graphs are coustructed and classification of small order hypergroups is discussed.The text of the thesis is arranged in four chapters. The first chapter is on preliminaries of the theory of hypergroups, the second on the appli- cation of the theory of hyjrrgroups …
Coxeter Groups And Positive Matrices., Arbind Kumar Lal Dr.
Coxeter Groups And Positive Matrices., Arbind Kumar Lal Dr.
Doctoral Theses
In this thesis, we study positive matrices (matrices whose entries are nonnegative as well as matrices which are positive semidefinite) with Coxeter groups as the underlying theme. For an exposition on Coxeter groups see Humphreys (1990).A Cozeter system consists of a pair (W, s); where W is a group and S is a set which consists of the generators of the group W. The elements of the set S have only the relations of the form (ss')m(s.) 1; where m(s, s) 1, m(s, s') = m(s,s) 2 2 for s s in S. In case no relation occurs for a …
Some External Problems And Charecterization In The Theory Of Graphs., Ramachandra Rao Dr.
Some External Problems And Charecterization In The Theory Of Graphs., Ramachandra Rao Dr.
Doctoral Theses
Graph theory has become such a well known and widely applied subject that it is not nocessary to give a general Introduetion to it. Instead ve eive helov a summary of the results of the thesis chapterwise.The study of extremal problems in Graph theory was started by Turan who deternined the minimum independence number of a graph on n vertices vith m edges. More recently Harary determined the maxinum conneetivity of a graph on n vortices vith m edges.In a paper concerning the degrees of the vertices of a graphy laktnd posed the following two problems : dotermin the maximum …
Studies In The Theory Of Graphs., R. P. Gupta Dr.
Studies In The Theory Of Graphs., R. P. Gupta Dr.
Doctoral Theses
No abstract provided.
External Graph Theoretic Problems With Applications To Communication Networks., Ramachandra Muthy Dr.
External Graph Theoretic Problems With Applications To Communication Networks., Ramachandra Muthy Dr.
Doctoral Theses
Graphs havre now become recognized models for a wide variety of situations. Whenever we have a collection of è´¸bjects with a binary relation defined on them graphs serve as excellopt toola to study the combinatoria properties of the collection with respect to the binary relation. D. Konig was the firat person to recognize the usefulness of graph theoretic modols. He conceived of a unified study of grapha under an abstract set up. His book was a pioneering work in this field.The graph theoretic problems embodied in this thesis have been motivated, by situations arising in communicationhave been motivated, by situations …