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In this book authors introduce the notion of subset vertex multigraphs for the first time. The study of subset vertex graphs was introduced in 2018, however they are not multiedged, further they were unique once the vertex subsets are given. These subset vertex multigraphs are also unique once the vertex subsets are given and the added advantage is that the number of common elements between two vertex subsets accounts for the number of edges between them, when there is no common element there is no edge between them.
In this book authors study special type of subset vertex multi subgraphs; these multi subgraphs can be directed or otherwise. Another special feature of these subset vertex multigraphs is that we are aware of the elements in each vertex set and how it affects the structure of both subset vertex multisubgraphs and edge multisubgraphs. It is pertinent to record at this juncture that certain ego centric directed multistar graphs become empty on the removal of one edge, there by theorising the importance, and giving certain postulates how to safely form ego centric multi networks.
The plithogenic set is a generalization of crisp, fuzzy, intuitionistic fuzzy, and Neutrosophic sets, it is a set whose elements are characterized by many attributes' values. This book gives some possible applications of plithogenic sets defined by Florentin Smarandache (2018). The authors have defined a new class of special type of graphs which can be applied for plithogenic models.
In this book any network which can be represented as a multigraph is referred to as a multi network. Several properties of multigraphs have been described and developed in this book. When multi path or multi walk or multi trail is considered in a multigraph, it is seen that there can be many multi walks, and so on between any two nodes and this makes multigraphs very different.
The shortest path problem is a topic of increasing interest in various scientific fields. The damage to roads and bridges caused by disasters makes traffic routes that can be accurately expressed become indeterminate. A neutrosophic set is a collection of the truth membership, indeterminacy membership, and falsity membership of the constituent elements. It has a symmetric form and indeterminacy membership is their axis of symmetry. In uncertain environments, the neutrosophic number can more effectively express the edge distance.
Already an international bestseller, with the release of this greatly enhanced second edition, Graph Theory and Its Applications is now an even better choice as a textbook for a variety of courses -- a textbook that will continue to serve your students as a reference for years to come. The superior explanations, broad coverage, and abundance of illustrations and exercises that positioned this as the premier graph theory text remain, but are now augmented by a broad range of improvements. Nearly 200 pages have been added for this edition, including nine new sections and hundreds of new exercises, mostly non-routine. What else is new? New chapters on measurement and analytic graph theory Supplementary exercises in each chapter - ideal for reinforcing, reviewing, and testing. Solutions and hints, often illustrated with figures, to selected exercises - nearly 50 pages worth Reorganization and extensive revisions in more than half of the existing chapters for smoother flow of the exposition Foreshadowing - the first three chapters now preview a number of concepts, mostly via the exercises, to pique the interest of reader Gross and Yellen take a comprehensive approach to graph theory that integrates careful exposition of classical developments with emerging methods, models, and practical needs. Their unparalleled treatment provides a text ideal for a two-semester course and a variety of one-semester classes, from an introductory one-semester course to courses slanted toward classical graph theory, operations research, data structures and algorithms, or algebra and topology.
This book provides a timely overview of fuzzy graph theory, laying the foundation for future applications in a broad range of areas. It introduces readers to fundamental theories, such as Craine’s work on fuzzy interval graphs, fuzzy analogs of Marczewski’s theorem, and the Gilmore and Hoffman characterization. It also introduces them to the Fulkerson and Gross characterization and Menger’s theorem, the applications of which will be discussed in a forthcoming book by the same authors. This book also discusses in detail important concepts such as connectivity, distance and saturation in fuzzy graphs. Thanks to the good balance between the basics of fuzzy graph theory and new findings obtained by the authors, the book offers an excellent reference guide for advanced undergraduate and graduate students in mathematics, engineering and computer science, and an inspiring read for all researchers interested in new developments in fuzzy logic and applied mathematics.
Studies to neutrosophic graphs happens to be not only innovative and interesting, but gives a new dimension to graph theory. The classic coloring of edge problem happens to give various results. Neutrosophic tree will certainly find lots of applications in data mining when certain levels of indeterminacy is involved in the problem. Several open problems are suggested.
Algebra | Partial Fractions | The Binomial Theorem | Exponential Theorem | The Logarithmic Series Theory Of Equations | Theory Of Equations | Reciprocal Equations | Newton-Rahson Method Matrices | Fundamental Concepts | Rank Of A Matrix | Linear Equations | Characteristic Roots And Vectors Finite Differences | Finite Differences | Interpolations: Newton'S Forward, Backward Interpolation | Lagrange'S Interpolation Trigonometry | Expansions | Hyperbolic Functions Differential Calculus | Successive Derivatives | Jacobians | Polar Curves Etc..
Some of the most beautiful studies in Mathematics are related to Symmetry and Geometry. For this reason, we select here some contributions about such aspects and Discrete Geometry. As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we consider network structures, symmetry means invariance of adjacency of nodes under the permutations of node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs. The automorphism of a graph will be an isomorphism from G onto itself. The family of all automorphisms of a graph G is a permutation group.