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Author : Fatemeh Alinaghipour Taklimi
Release : 2014
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Zero Forcing Sets for Graphs by : Fatemeh Alinaghipour Taklimi
Download or read book Zero Forcing Sets for Graphs written by Fatemeh Alinaghipour Taklimi. This book was released on 2014. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Leslie Hogben
Release : 2022-07-21
Genre : Mathematics
Kind : eBook
Book Rating : 554/5 ( reviews)
Book Synopsis Inverse Problems and Zero Forcing for Graphs by : Leslie Hogben
Download or read book Inverse Problems and Zero Forcing for Graphs written by Leslie Hogben. This book was released on 2022-07-21. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the inverse eigenvalue problem for graphs (IEP-$G$) and the related area of zero forcing, propagation, and throttling. The IEP-$G$ grew from the intersection of linear algebra and combinatorics and has given rise to both a rich set of deep problems in that area as well as a breadth of “ancillary” problems in related areas. The IEP-$G$ asks a fundamental mathematical question expressed in terms of linear algebra and graph theory, but the significance of such questions goes beyond these two areas, as particular instances of the IEP-$G$ also appear as major research problems in other fields of mathematics, sciences and engineering. One approach to the IEP-$G$ is through rank minimization, a relevant problem in itself and with a large number of applications. During the past 10 years, important developments on the rank minimization problem, particularly in relation to zero forcing, have led to significant advances in the IEP-$G$. The monograph serves as an entry point and valuable resource that will stimulate future developments in this active and mathematically diverse research area.
Author :
Release : 2012
Genre :
Kind : eBook
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Book Synopsis Zero Forcing Sets and Bipartite Circulants by :
Download or read book Zero Forcing Sets and Bipartite Circulants written by . This book was released on 2012. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis we introduce a class of regular bipartite graphs whose biadjacency matrices are circulant matrices -- a generalization of circulant graphs which happen to be bipartite -- and we describe some properties possessed by these graphs. We describe sufficient conditions for two of these graphs to be isomorphic and prove necessary conditions in some cases. We also compute upper and lower bounds for the zero forcing number of such a graph based only on the parameters that describe its biadjacency matrix. The main results of this thesis characterize the bipartite circulant graphs that achieve equality in the lower bound and compute their minimum ranks.
Author : TeresaW. Haynes
Release : 2017-11-22
Genre : Mathematics
Kind : eBook
Book Rating : 641/5 ( reviews)
Book Synopsis Domination in Graphs by : TeresaW. Haynes
Download or read book Domination in Graphs written by TeresaW. Haynes. This book was released on 2017-11-22. Available in PDF, EPUB and Kindle. Book excerpt: ""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. Covers recent developments in domination in graphs and digraphs, dominating functions, combinatorial problems on chessboards, and more.
Author : Jakob Loedding
Release : 2022
Genre :
Kind : eBook
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Book Synopsis Optimization Applied in Graph Theory by : Jakob Loedding
Download or read book Optimization Applied in Graph Theory written by Jakob Loedding. This book was released on 2022. Available in PDF, EPUB and Kindle. Book excerpt: Zero-forcing is a coloring game on a graph in which an initial set of vertices is colored gray while the remaining vertices are colored white. An iterative color change rule, where some vertices have the ability to force others to change their color to gray, is then applied until no more vertices may be forced. A zero-forcing set of a graph G is defined as an initial set of gray vertices in which the remaining white vertices are forced gray after some number of iterations of the color change rule. The minimum cardinality of a zero-forcing set is defined as the zero-forcing number of G. In this thesis, we define a new graph parameter called the zero-forcing diameter, which quan- tifies the minimum intersection of two minimum zero-forcing sets of a graph with respect to its zero-forcing number. Furthermore, we present the numerical bounds of the zero-forcing diameter and find its value, with theoretical proof, for specific graph families. We then introduce an integer programming model for calculating the zero-forcing number of a graph. Finally, we build upon this model to develop our own integer program for calculating the zero-forcing diameter of a graph.
