On Isomorphic Decompositions Of Graphs
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On Isomorphic Decompositions Of Graphs
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Author : Sergio Ruiz
language : en
Publisher:
Release Date : 1983
On Isomorphic Decompositions Of Graphs written by Sergio Ruiz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Graph theory categories.
Decompositions Of Graphs
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Author : Juraj Bosák
language : en
Publisher: Taylor & Francis US
Release Date : 1990
Decompositions Of Graphs written by Juraj Bosák and has been published by Taylor & Francis US this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
Graph Theory And Decomposition
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Author : Jomon Kottarathil
language : en
Publisher: CRC Press
Release Date : 2024-04-10
Graph Theory And Decomposition written by Jomon Kottarathil and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-10 with Mathematics categories.
The book Graph Theory and Decomposition covers major areas of the decomposition of graphs. It is a three-part reference book with nine chapters that is aimed at enthusiasts as well as research scholars. It comprehends historical evolution and basic terminologies, and it deliberates on decompositions into cyclic graphs, such as cycle, digraph, and K4-e decompositions. In addition to determining the pendant number of graphs, it has a discourse on decomposing a graph into acyclic graphs like general tree, path, and star decompositions. It summarises another recently developed decomposition technique, which decomposes the given graph into multiple types of subgraphs. Major conjectures on graph decompositions are elaborately discussed. It alludes to a comprehensive bibliography that includes over 500 monographs and journal articles. It includes more than 500 theorems, around 100 definitions, 56 conjectures, 40 open problems, and an algorithm. The index section facilitates easy access to definitions, major conjectures, and named theorems. Thus, the book Graph Theory and Decomposition will be a great asset, we hope, in the field of decompositions of graphs and will serve as a reference book for all who are passionate about graph theory.
Decompositions Of Complete Multipartite Graphs And Group Divisible Designs Into Isomorphic Factors
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Author : Dalibor Fronček
language : en
Publisher:
Release Date : 1994
Decompositions Of Complete Multipartite Graphs And Group Divisible Designs Into Isomorphic Factors written by Dalibor Fronček and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Decomposition (Mathematics) categories.
Canonical Graph Decomposition In Matching
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Author :
language : en
Publisher:
Release Date : 2004
Canonical Graph Decomposition In Matching written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.
In the following thesis, we present our proposed probabilistic approach to the graph isomorphism problem. Through a "divide and conquer" approach, a graph is first decomposed into unique subgraphs, termed atoms, that are used to represent a decomposed graph as a bipartite attributed graph. We propose a modified probabilistic relaxation that simulates belief propagation and operates on the generated bipartite graph, yielding a match matrix that maps together isomorphic atoms from different graphs. Our proposed approach enforces a two way matching constraint thatguarantees a one-to-one match between isomorphic atoms. On average, the approach converges for isomorphic graphs and diverges for non-isomorphic graphs.
The Theory Of 2 Structures
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Author : Andrzej Ehrenfeucht
language : en
Publisher: World Scientific
Release Date : 1999
The Theory Of 2 Structures written by Andrzej Ehrenfeucht and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
The theory of 2-structures provides a convenient framework for decomposition and transformation of mathematical systems where one or several different binary relationships hold between the objects of the system. In particular, it forms a useful framework for decomposition and transformation of graphs. The decomposition methods presented in this book correspond closely to the top-down design methods studied in theoretical computer science. The transformation methods considered here have a natural interpretation in the dynamic evolution of certain kinds of communication networks. From the mathematical point of view, the clan decomposition method presented here, also known as modular decomposition or substitution decomposition, is closely related to the decomposition by quotients in algebra. The transformation method presented here is based on labelled 2-structures over groups, the theory of which generalizes the well-studied theory of switching classes of graphs. This book is both a text and a monograph. As a monograph, the results concerning the decomposition and transformation of 2-structures are presented in a unified way. In addition, detailed notes on references are provided at the end of each chapter. These notes allow the reader to trace the origin of many notions and results, and to browse through the literature in order to extend the material presented in the book. To facilitate its use as a textbook, there are numerous examples and exercises which provide an opportunity for the reader to check his or her understanding of the discussed material. Furthermore, the text begins with preliminaries on partial orders, semigroups, groups and graphs to the extent needed for the book.
Automorphism Decompositions Of Graphs
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Author : Cara M. Wiblemo
language : en
Publisher:
Release Date : 2010
Automorphism Decompositions Of Graphs written by Cara M. Wiblemo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Automorphisms categories.
A graph has an automorphism decomposition if its adjacency matrix can be written as the sum of permutation matrices, each of which is an automorphism of the graph. These graphs appear to be closely related to Cayley graphs. This paper investigates the properties of graphs with automorphism decompositions. Each must be k-regular, and each edge in such a graph must be in at least (k-2) 4-cycles. We show that graphs that are isomorphic to Cayley graphs on abelian groups always have automorphism decompositions, and all 3-regular graphs with automorphism decompositions are Cayley graphs on abelian groups. Additionally, we investigate the connection to covering graphs.
The Theory Of 2 Structures
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Author : A Ehrenfeucht
language : en
Publisher: World Scientific Publishing Company
Release Date : 1999-08-30
The Theory Of 2 Structures written by A Ehrenfeucht and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-08-30 with Mathematics categories.
The theory of 2-structures provides a convenient framework for decomposition and transformation of mathematical systems where one or several different binary relationships hold between the objects of the system. In particular, it forms a useful framework for decomposition and transformation of graphs. The decomposition methods presented in this book correspond closely to the top-down design methods studied in computer science. The transformation methods considered here have a natural interpretation in the dynamic evolution of certain kinds of communication networks. From the mathematical point of view, the clan decomposition method presented here, also known as modular decomposition or substitution decomposition, is closely related to the decomposition by quotients in algebra. The transformation method presented here is based on labelled 2-structures over groups, the theory of which generalizes the well-studied theory of switching classes of graphs. This book is both a text and a monograph. As a monograph, the results concerning the decomposition and transformation of 2-structures are presented in a unified way. In addition, detailed notes on references are provided at the end of each chapter. These notes allow the reader to trace the origin of many notions and results, and to browse through the literature in order to extend the material presented in the book. To facilitate its use as a textbook, there are numerous examples and exercises which provide an opportunity for the reader to check his or her understanding of the discussed material. Furthermore, the text begins with preliminaries on partial orders, semigroups, groups and graphs to the extent needed for the book. Request Inspection Copy
Localized Structure In Graph Decompositions
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Author : Flora Caroline Bowditch
language : en
Publisher:
Release Date : 2019
Localized Structure In Graph Decompositions written by Flora Caroline Bowditch and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
Let v ∈ Z+ and G be a simple graph. A G-decomposition of Kv is a collection F={F1,F2,...,Ft} of subgraphs of Kv such that every edge of Kv occurs in exactlyone of the subgraphs and every graph Fi ∈ F is isomorphic to G. A G-decomposition of Kv is called balanced if each vertex of Kv occurs in the same number of copies of G. In 2011, Dukes and Malloch provided an existence theory for balanced G-decompositions of Kv. Shortly afterwards, Bonisoli, Bonvicini, and Rinaldi introduced degree- and orbit-balanced G-decompositions. Similar to balanced decompositions,these two types of G-decompositions impose a local structure on the vertices of Kv. In this thesis, we will present an existence theory for degree- and orbit-balanced G-decompositions of Kv. To do this, we will first develop a theory for decomposing Kv into copies of G when G contains coloured loops. This will be followed by a brief discussion about the applications of such decompositions. Finally, we will explore anextension of this problem where Kv is decomposed into a family of graphs. We will examine the complications that arise with families of graphs and provide results for a few special cases.
The Graph Isomorphism Algorithm
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Author : Ashay Dharwadker
language : en
Publisher: Institute of Mathematics
Release Date : 2009-08-08
The Graph Isomorphism Algorithm written by Ashay Dharwadker and has been published by Institute of Mathematics this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-08 with Mathematics categories.
We present a new polynomial-time algorithm for determining whether two given graphs are isomorphic or not. We prove that the algorithm is necessary and sufficient for solving the Graph Isomorphism Problem in polynomial-time, thus showing that the Graph Isomorphism Problem is in P. The semiotic theory for the recognition of graph structure is used to define a canonical form of the sign matrix of a graph. We prove that the canonical form of the sign matrix is uniquely identifiable in polynomial-time for isomorphic graphs. The algorithm is demonstrated by solving the Graph Isomorphism Problem for many of the hardest known examples. We implement the algorithm in C++ and provide a demonstration program for Microsoft Windows.