The Use of Adjacency Series for Recognition of Prefractal Graphs in Assessing VANET Cybersecurity

Zegzhda, Peter D.; Иванов, Д.; Moskvin, Dmitry A.; Ivanov, A. A.

doi:10.3103/s0146411618080266

Cited by 2 publications

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“…In the terminology of prefractal graphs [20][21][22], the families of self-similar graphs, such as Farey graphs, 2-dimensional Sierpi ński gasket graphs, Hanoi graphs, modified Koch graphs, Apollonian graphs, pseudofractal scale-free webs, fractal scale-free networks, etc. [23][24][25], are noncanonical prefractal graphs.…”

Section: Introductionmentioning

confidence: 99%

Introduction to the Class of Prefractal Graphs

Kochkarov

2022

Mathematics

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Fractals are already firmly rooted in modern science. Research continues on the fractal properties of objects in physics, chemistry, biology and many other scientific fields. Fractal graphs as a discrete representation are used to model and describe the structure of various objects and processes, both natural and artificial. The paper proposes an introduction to prefractal graphs. The main definitions and notation are proposed—the concept of a seed, the operations of processing a seed, the procedure for generating a prefractal graph. Canonical (typical) and non-canonical (special) types of prefractal graphs are considered separately. Important characteristics are proposed and described—the preservation of adjacency of edges for different ranks in the trajectory. The definition of subgraph-seeds of different ranks is given separately. Rules for weighting a prefractal graph by natural numbers and intervals are proposed. Separately, the definition of a fractal graph as infinite is given, and the differences between the concepts of fractal and prefractal graphs are described. At the end of the work, already published works of the authors are proposed, indicating the main backlogs, as well as a list of directions for new research. This work is the beginning of a cycle of works on the study of the properties and characteristics of fractal and prefractal graphs.

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Section: Introductionmentioning

confidence: 99%

Introduction to the Class of Prefractal Graphs

Kochkarov

2022

Mathematics

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“…Prefractal graphs [20][21][22] represent a relatively new subclass of large dynamic graphs [23][24][25]. With large prefractal graphs, it is possible to build graph-theoretic models of the structure of social networks and solve various optimization problems on them [26][27][28]-finding the shortest paths, highlighting subgraphs, multicriteria optimization, etc.…”

Section: Introductionmentioning

confidence: 99%

Research of NP-Complete Problems in the Class of Prefractal Graphs

Kochkarov

2021

Mathematics

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NP-complete problems in graphs, such as enumeration and the selection of subgraphs with given characteristics, become especially relevant for large graphs and networks. Herein, particular statements with constraints are proposed to solve such problems, and subclasses of graphs are distinguished. We propose a class of prefractal graphs and review particular statements of NP-complete problems. As an example, algorithms for searching for spanning trees and packing bipartite graphs are proposed. The developed algorithms are polynomial and based on well-known algorithms and are used in the form of procedures. We propose to use the class of prefractal graphs as a tool for studying NP-complete problems and identifying conditions for their solvability. Using prefractal graphs for the modeling of large graphs and networks, it is possible to obtain approximate solutions, and some exact solutions, for problems on natural objects—social networks, transport networks, etc.

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The Use of Adjacency Series for Recognition of Prefractal Graphs in Assessing VANET Cybersecurity

Cited by 2 publications

References 1 publication

Introduction to the Class of Prefractal Graphs

Introduction to the Class of Prefractal Graphs

Research of NP-Complete Problems in the Class of Prefractal Graphs

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