Locality-constrained discrete graph hashing

2019 ◽

Vol 35 (2) ◽

pp. 137-146

Author(s):

STEFAN BEREZNY ◽

MICHAL STAS ◽

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Keyword(s):

Crossing Number ◽

Crossing Numbers ◽

Symmetric Graphs ◽

Isolated Vertex ◽

Join Of Graphs ◽

Discrete Graph

The main purpose of this article is broaden known results concerning crossing numbers for join of graphs of order six. We give the crossing number of the join product G + Dn, where the graph G consists of one 5-cycle and of one isolated vertex, and Dn consists on n isolated vertices. The proof is done with the help of software that generates all cyclic permutations for a given number k, and creates a new graph COG for calculating the distances between all vertices of the graph. Finally, by adding some edges to the graph G, we are able to obtain the crossing numbers of the join product with the discrete graph Dn and with the path Pn on n vertices for other two graphs.

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On the crossing number of join of the wheel on six vertices with the discrete graph

Carpathian Journal of Mathematics ◽

10.37193/cjm.2020.03.06 ◽

2020 ◽

Vol 36 (3) ◽

pp. 381-390

Author(s):

STEFAN BEREZNY ◽

MICHAL STAS

Keyword(s):

Crossing Number ◽

Discrete Graph

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On the crossing numbers of join products of five graphs of order six with the discrete graph

Opuscula Mathematica ◽

10.7494/opmath.2020.40.3.383 ◽

2020 ◽

Vol 40 (3) ◽

pp. 383

Author(s):

Michal Staš

Keyword(s):

Crossing Numbers ◽

Discrete Graph

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Topology Attack and Defense for Graph Neural Networks: An Optimization Perspective

Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence ◽

10.24963/ijcai.2019/550 ◽

2019 ◽

Cited By ~ 10

Author(s):

Kaidi Xu ◽

Hongge Chen ◽

Sijia Liu ◽

Pin-Yu Chen ◽

Tsui-Wei Weng ◽

...

Keyword(s):

Neural Networks ◽

Classification Performance ◽

Original Graph ◽

Graph Data ◽

Gradient Based ◽

Significant Performance ◽

Adversarial Training ◽

Graph Neural Networks ◽

Attack And Defense ◽

Discrete Graph

Graph neural networks (GNNs) which apply the deep neural networks to graph data have achieved significant performance for the task of semi-supervised node classification. However, only few work has addressed the adversarial robustness of GNNs. In this paper, we first present a novel gradient-based attack method that facilitates the difficulty of tackling discrete graph data. When comparing to current adversarial attacks on GNNs, the results show that by only perturbing a small number of edge perturbations, including addition and deletion, our optimization-based attack can lead to a noticeable decrease in classification performance. Moreover, leveraging our gradient-based attack, we propose the first optimization-based adversarial training for GNNs. Our method yields higher robustness against both different gradient based and greedy attack methods without sacrifice classification accuracy on original graph.

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On the crossing number of the join of the discrete graph with one graph of order ﬁve

Mathematical Modelling and Geometry ◽

10.26456/mmg/2017-522 ◽

2017 ◽

Vol 5 (2) ◽

Cited By ~ 3

Author(s):

Michal Staš

Keyword(s):

Crossing Number ◽

Discrete Graph

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Formalization and Discrete Modelling of Communication in the Digital Age by Using Graph Theory

Handbook of Research on Advanced Applications of Graph Theory in Modern Society - Advances in Computer and Electrical Engineering ◽

10.4018/978-1-5225-9380-5.ch013 ◽

2020 ◽

pp. 320-353

Author(s):

Radi Petrov Romansky

Keyword(s):

Graph Theory ◽

Modern Society ◽

Digital Age ◽

Information Resources ◽

Remote Access ◽

Network Resources ◽

Digital Representation ◽

Discrete Modelling ◽

Key Features ◽

Discrete Graph

Globalization is an important characteristic of the digital age which is based on the informatization of the society as a social-economical and science-technical process for changing the information environment while keeping the rights of citizens and organizations. The key features of the digital age are knowledge orientation, digital representation, virtual and innovative nature, integration and inter-network interactions, remote access to the information resources, economic and social cohesion, dynamic development, etc. The graph theory is a suitable apparatus for discrete presentation, formalization, and model investigation of the processes in the modern society because each state of a process could be presented as a node in a discrete graph with connections to other states. The chapter discusses application of the graph theory for a discrete formalization of the communication infrastructure and processes for remote access to information and network resources. An extension of the graph theory like apparatus of Petri nets is discussed and some examples for objects investigation are presented.

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