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Saturday, July 11, 2020 | History

5 edition of Domination in graphs found in the catalog.

Domination in graphs

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Published by Marcel Dekker in New York .
Written in English

    Subjects:
  • Domination (Graph theory)

  • Edition Notes

    Includes index.

    Statementedited by Teresa W. Haynes, Stephen T. Hedetniemi, Peter J. Slater.
    SeriesMonographs and textbooks in pure and applied mathematics ;, 209
    ContributionsHaynes, Teresa W., 1953-, Hedetniemi, S. T., Slater, Peter J.
    Classifications
    LC ClassificationsQA166 .D655 1997
    The Physical Object
    Paginationxii, 497 p. :
    Number of Pages497
    ID Numbers
    Open LibraryOL696019M
    ISBN 100824700341
    LC Control Number97043491

    Discusses graph domination. This book covers various developments in domination in graphs and digraphs, dominating functions, and combinatorial problems on chessboards. Read more. Connected Domination in Graphs Gayathri Mahalingam ABSTRACT A connected dominating set D is a set of vertices of a graph G = (V;E) such that every vertex in V ¡ D is adjacent to at least one vertex in D and the sub- graph hDi induced by the set D is connected. The connected domination number °c(G) is the minimum of the cardinalities of the connected dominating sets of G.

    The complementary edge domination in graphs is studied by Kulli and Soner [18] The edge domination in graphs of cubes and Signed total domination is studied by Zelinka [24,25]. Books shelved as graph-theory: Introductory Graph Theory by Gary Chartrand, Handbook of Graphs and Networks: From the Genome to the Internet by Stefan Bo.

    Graph Theory Books. This section contains free e-books and guides on Graph Theory, some of the resources in this section can be viewed online and some of them can be downloaded. Descriptive Complexity, Canonisation, and Definable Graph Structure Theory. The contributions in this volume are divided into three sections: theoretical, new models and algorithmic. The first section focuses on properties of the standard domination number &ggr;(G), the second section is concerned with new variations on the domination theme, and the third is primarily concerned with finding classes of graphs for which the domination number (and several other.


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Domination in graphs Download PDF EPUB FB2

Total Domination in Graphs gives a clear understanding  of this topic to any interested reader who has a modest background in graph theory. This book provides and explores the fundamentals of total domination in by: Provides the first comprehensive treatment of theoretical, algorithmic, and application aspects of domination in graphs-discussing fundamental results and major research accomplishments in an easy-to-understand style.

Includes chapters on domination algorithms and NP-completeness as well as frameworks for domination/5(6). He coauthored, the first book on domination in Fundamentals of Domination in Graphs, and co-edited a second book, Domination in Graphs: Advanced Topics. He also co-edited 2 volumes in Springer’s Problem Books in Mathematics Graph Theory: Favorite Conjectures and Open Problems.

Since he has coauthored more than papers, of which are on domination and domination-related. Book Description "Provides the first comprehensive treatment of theoretical, algorithmic, and application aspects of domination in graphs-discussing fundamental results and major research accomplishments in an easy-to-understand style.

Includes chapters on domination algorithms Domination in graphs book NP-completeness as well as frameworks for domination.". ""Presents the latest in graph domination by leading researchers from around the world-furnishing known results, open research problems, and proof techniques.

Maintains standardized terminology and notation throughout for greater by: 5. It is clear from the content of this and the accompanying book that domination in graphs, along with its many variations, provides an extremely rich area of study.

In India, interest in modern domination in graphs was triggered by the monograph-cum-thesis of Walikar. This chapter surveys several topics in the field introduced since : E.

Sampathkumar. This book provides and explores the fundamentals of total domination in graphs. Some of the topics featured include the interplay between total domination in graphs and transversals in hypergraphs, and the association with total domination in graphs and diametercritical graphs.

Abstract “Domination in graphs” is an area of graph theory that has received a lot of attention in recent years. It is reasonable to believe that “domination in graphs” has its origin in “chessboard domination.”Author: R.

Balakrishnan, K. Ranganathan. First, two of the fundamental domination numbers are not de ned for graphs with isolated vertices. Second, if Gis disconnected and has no isolated vertices, then the value of each of the fundamental domination numbers for Gis equal to the sum of the values of the same number for each 3 of the connected components of G.

The editors have collected a set of research papers on graph domination. This book is a companion to "Fundamentals of Domination in Graphs" by the same editors. Readers might well want to consult both books.

The book is best suited to a reader majoring in maths or computer by: Appropriate for use at different levels, Fundamentals of Domination in Graphs reinforces the material with a host of learning and pedagogical features, such as basic definitions and preliminary graph theoretic results consistent graph theory terminology throughout the work end-of-chapter exercises and problems as well as noteworthy open.

"Provides the first comprehensive treatment of theoretical, algorithmic, and application aspects of domination in graphs-discussing fundamental results and major research accomplishments in an 3/5(4). Book Description "Presents the latest in graph domination by leading researchers from around the world-furnishing known results, open research problems, and proof techniques.

Maintains standardized terminology and notation throughout for greater accessibility. The recent book Fundamentals of Domination in Graphs lists, in an appendix, many varieties of dominating sets that have been studied.

It appears that none of those listed are the same as Roman dominating sets. Thus, Roman domination appears to be a new variety of both historical and mathematical interest.

Properties of Roman dominating sets. not contain a graph F as an induced subgraph, then we say that Gis F-free. In particular, we say that a graph is claw-free if it is K 1;3-free. Common Graphs and Exact Values The independent domination number of some common graphs is given in Proposi-tion Proposition (a) For the path and cycle, i(P n) = i(C n) = dn=3e.

A graph G is a domination graph if every induced subgraph H of G contains a pair of vertices x, y such that in H the neighborhood of x is contained in the closed neighborhood of y; i.e. NH (x) is a subset of NH (y)∪ { y } (in this case, x is said to be dominated by y in H).

Description "Presents the latest in graph domination by leading researchers from around the world-furnishing known results, open research problems, and proof techniques. Maintains 3/5(1). The study of domination in graphs originated around with the problems of placing minimum number of queens or other chess pieces on an n.

Presents theoretical, algorithmic, and application aspects of domination in graphs - discussing fundamental results and major research accomplishments. This book includes chapters on domination.

algorithms and NP-completeness as well as frameworks for domination. ABSTRACT: Vizing conjectured in that the domination number of the Cartesian product of two graphs is at least the product of their domination numbers; this remains one of the biggest open problems in the study of domination in graphs.

Several partial results have been proven, but the conjecture has yet to be proven in general. Domination is an area in graph theory with an extensive research activity. Ina book [HHS98] on domination has been published which lists papers in this area.

In general, a dominating set in a graph is a set of vertices D such that each vertex is either .A set D of vertices of a finite, undirected graph G = (V, E) is a total dominating set if every vertex of V is adjacent to some vertex of this paper we initiate the study of total dominating sets in graphs and, in particular, obtain results concerning the total domination number of G (the smallest number of vertices in a total dominating set) and the total domatic number of G (the largest.Total Domination in Graphs gives a clear understanding of this topic to any interested reader who has a modest background in graph theory.

This book provides and explores the fundamentals of total domination in graphs. Some of the topics featured include the interplay between total domination in graphs and transversals.