Purpose: The objective of this research is to study and compare the coauthorship Graphs (networks) of Iranian researchers in the main fields of mathematics by using records, extracted from WOS and Google Scholar, and Graph parameters. Methodology: The co-authorship Graphs (networks) of Iranian researchers in 6 specialty fields of mathematics have been drawn by mathematical methods and software. Overall this research, 276 Iranian researchers in mathematics were considered and the co-authorship Graphs in all fields were drawn and compared. Some mathematical Graph parameters such as degrees of vertices, diameter, radius, independence number, vertex and edge chromatic numbers, matching number, for all co-authorship Graphs were calculated too. Finally, we analyze and compare the co-authorship Graphs by using these Graph parameters. Findings: The research findings showed that two specialty fields Operation Research and Graphs and Combinatorics with average degrees 4. 20 and 3. 70, respectively, have high research collaboration with respect to other fields. The greatest diameter in the co-authorship Graph, which equals 8, belongs to Commutative Algebra and the co-authorship Graphs of the specialty field Numerical Analysis and Group Theory have the same least value of radius 3. Conclustion: In some specialty fields of mathematics, which are pure, there is not enough collaboration among Iranian researchers. So, it is better that these researchers try to have more collaboration to publish stronger and deeper research works in the international journals. For this aim, more budget allocations should be considered to accelerate researchers to do group works with high quality.

Chemical Graph theory is a bridge between Chemistry and Graph theory. Graph energies are important tools for QSPR researches. Thus, this study aims to relate several energies with the QSPR Analysis of 67 alkanes. We compare these results with the Maximum Degree Energy, Minimum Degree Energy, and Second Zagreb Energy. Our study reveals some interesting results based on the predicting power of these Graph energies.AMS 2010 codes:  94C15, 92E10.

Despite several studies and attempts, in time-memory trade-off attacks on cryptoGraphic algorithms, the coverage of Hellman tables and similar methods are practically much less than half and their probability of success is low. In fact, Hellman chains are paths with given starting and end vertices on a functional Graph. In this paper, behavior of these chains is investigated with this approach. In the beginning of the paper, parameters of the functional Graph for a random mapping are defined and based on these parameters, Hellman chains are analyzed. Our results show that the coverage of such tables can’t be high, for the following reasons: First, there exist some remarkable terminal vertices (37%) on the functional Graph such that the possible occurrence of these vertices on chains (except in the starting vertices) is zero. Secondly, appropriate parameters for constructing chains exist in Graph for about half of all hidden states of cipher function. Thirdly, for construction of noncyclic chains and collision of chains, we must pay attention to the obtained probabilities in this note. Practically, above reasons show that after some point the coverage of a Hellman table tends to zero quickly, and so construction of them will be ineffective. Our results are implemented on mAES algorithm where validate our theatrical results.

Background: Autism spectrum disorder is a neurodevelopmental condition in which impaired connectivity of the brain network. The functional magnetic resonance imaging (fMRI) technique can provide information on the early diagnosis of autism by evaluating communication patterns in the brain. The present study aimed to assess functional connectivity (FC) variations in autism patients. Materials and Methods: Resting? state fMRI data were obtained from the “ABIDE” website. These data include 294 autism patients with a mean (standard deviation) age of 16. 49 (7. 63) and 312 healthy individuals with a mean (standard deviation) age of 15. 98 (6. 31). In this study, changes in communication patterns across different brain regions in autism patients were investigated using Graph? based models. Results: The FC cluster of 17 regions in the brain, such as the ippocampus, cuneus, and inferior temporal, was different between the patient and healthy groups. Based on connectivity Analysis of pair regions, 36 of the 136 correlations in the cluster were significantly different between the two groups. The middle temporal gyrus had more communication than the other regions. The largest difference between groups was – 0. 112, which corresponding to the right middle temporal and right thalamus regions. Conclusion: The findings of this study revealed functional relationship alterations in patients with autism compared to healthy individuals, indicating the disease’s effects on the brain connectivity network.

The independence Graph Ind(G) of a Graph G is the Graph with vertices as maximum independent sets of G and two vertices are adjacent, if and only if the corresponding maximum independent sets are disjoint. In this work, we find the independence Graph of Cartesian product of d copies of complete Graphs Kq, which is known as the Hamming Graph H(d, q). Greenwell and Lovasz [7] found that the independence number of direct product of d copies of Kq as qd−1. We prove that the independence number of Hamming Graph H(d, q), which is cartesian product of d copies of Kq, is also qd−1. As an application of our findings, we find answers for rook problem in higher dimensional square chess board.

In this paper, we consider the Time-Memory-Trade-Off (TMTO) method for Analysis of block ciphers and related methods. Also, we discuss some subjects including coverage in the Hellman chains, collision in chains, cycles and rings that create a block cipher function. Hellman method is analyzed by a random Graph. The random Graph is made of a function block cipher, which is applied to extract non-collision chains, cycles and rings. According to the unique modes and features available in the random Graph, a new method for extraction of cycles and rings in the random Graph entitled "agility of Graph" is offered. This meth-od extracts the cycles and rings of the lock cipher function as easily and at a very low cost. The obtained cycles and rings are used for generating non-collision chains in the block ciphers that they make a complete coverage of block ciphers in the TMTO method.

Today, increasing the science and technology and the communication technologies, especially in cyberspace, however physically act have become interact with cyberspace has caused a more significant effect on the culture and geoGraphy of each country. Accordingly, dealing with these physical crimes interacts with cyberspace. Therefore, detecting crimes and identifying criminals using old methods is almost impossible. Therefore, databases and their processing can play an essential role in detecting crime patterns for police-security organizations. The highly effective methods and tools of social network Analysis can discover the pattern and extract knowledge from the database to prevent and control crime. This article explores crime rules using social network Analysis methods and offers suggestions for preventing crimes and identifying perpetrators. The Analysis of social networks has great importance, and the results obtained from these analyzes can be used in similar applications. In this article, the first has been collected the data related to currency disruptors in recent years, then analyzed this data with social network techniques and identified compelling features for identifying virtual nodes. The results show that social network Analysis methods have simulated a model with acceptable accuracy and introduced destructive nodes by analyzing features. However, identifying destructive nodes and crime prevention can be considered, thoroughly describing how to do this in the paper.

There is a rapid increase in number and variety of malware. In particular, hundreds of thousands of new malware are observed on a daily basis. This amplifies the need for automatic Analysis and detection of malware. Recently, techniques based on system call dependency Graphs have emerged due to their promising detection rate and ease of implementation. In this paper, a new approach is proposed for malware detection. The approach is based on Analysis of system call dependency Graphs. Dependency frequencies are considered as feature vectors to represent malware and benign behavior. Given a train set of system call dependency Graphs from various benign and malware families, machine learning algorithms are used to construct classification models. We try algorithms such as support vector machines, random forests and gradient boosted decision trees and train various classification models. The evaluation results demonstrate that most of these models, in comparison with other related work, have a high degree of detection rate and low false positive rate.