A graph operation and its applications in generating orderenergetic and equienergetic graphs

A general graph operation is defined and some of its applications are given in this paper. The adjacency spectrum of any graph generated by this operation is given. A method for generating integral graphs using this operation is discussed. Corresponding to any given graph, we can generate an infinite sequence of pair of equienergetic non-cospectral graphs using this graph operation. Given an orderenergetic graph, it is shown that we can construct two different sequences of orderenergetic graphs. A condition for generating orderenergetic graphs from non-orderenergetic graphs are also derived. This method of constructing connected orderenergetic graphs solves one of the open problem stated in the paper by Akbari et al.(2020).

Asymmetric circular graph with Hosoya index and negative continued fractions

It has been known that the Hosoya index of caterpillar graph can be calculated as the numerator of the simple continued fraction. Recently in [MATCH Commun. Math. Comput. Chem. 2020, 84 (2), 399-428], the author introduces a more general graph called caterpillar-bond graph and shows that its Hosoya index can be calculated as the numerator of the general continued fraction. In this paper, we show how the Hosoya index of the graph with non-uniform ring structure can be calculated from the negative continued fraction. We also give the relation between some radial graphs and multidimensional continued fractions in the sense of the Hosoya index.

Methods and Tools for Visualization of Graphs and Graph Algorithms

Graphs are the most common abstract structure encountered in computer science and are widely used for structural information visualization. In the paper, we consider practical and general graph formalism of so called hierarchical graphs and present the Higres and ALVIS systems aimed at supporting of structural information visualization on the base of hierarchical graph models.

Solving Graph Homomorphism and Subgraph Isomorphism Problems Faster Through Clique Neighbourhood Constraints

Graph homomorphism problems involve finding adjacency-preserving mappings between two given graphs. Although theoretically hard, these problems can often be solved in practice using constraint programming algorithms. We show how techniques from the state-of-the-art in subgraph isomorphism solving can be applied to broader graph homomorphism problems, and introduce a new form of filtering based upon clique-finding. We demonstrate empirically that this filtering is effective for the locally injective graph homomorphism and subgraph isomorphism problems, and gives the first practical constraint programming approach to finding general graph homomorphisms.

Computation of Topological Indices of NEPS of Graphs

The inspection of the networks and graphs through structural properties is a broad research topic with developing significance. One of the methods in analyzing structural properties is obtaining quantitative measures that encode data of the whole network by a real quantity. A large quantity of graph-associated numerical invariants has been used to examine the whole structure of networks. In this analysis, degree-related topological indices have a significant place in nanotechnology and theoretical chemistry. Thereby, the computation of indices is one of the successful branches of research. The noncomplete extended p -sum NEPS of graphs is a famous general graph product. In this paper, we investigated the exact formulas of general zeroth-order Randić, Randić, and the first multiplicative Zagreb indices for NEPS of graphs.

Autonomous Unmanned Aerial Vehicle for Post-Disaster Management With Cognitive Radio Communication

Unmanned aerial vehicles (UAV) play a significant role in finding victims affected in the post-disaster zone, where a man cannot risk his life under a critical condition of the disaster environment. The proposed design incorporates autonomous vision-based navigation through the disaster environment based on general graph theory with dynamic changes on the length between two or multiple nodes, where a node is a pathway. Camera fixed on it continuously captures the surrounding footage, processing it frame by frame on-site using image processing technique based on a SOC. Identifies victims in the zone and the pathways available for traversal. UAV uses an ultrasonic rangefinder to avoid collision with obstacles. The system alerts the rescue team if any victim detected and transmits the frames using CRN to the off-site console. UAV learns navigation policy that achieves high accuracy in real-time environments; communication using CRN is uninterrupted and useful during such emergencies.

Graph Tools for Social Network Analysis

A social network can be defined as a complex graph, which is a collection of nodes connected via edges. Nodes represent individual actors or people in the network, whereas edges define relationships among those actors. Most popular social networks are Facebook, Twitter, and Google+. To analyze these social networks, one needs specialized tools for analysis. This chapter presents a comparative study of such tools based on the general graph aspects as well as the social network mining aspects. While considering the general graph aspects, this chapter presents a comparative study of four social network analysis tools—NetworkX, Gephi, Pajek, and IGraph—based on the platform, execution time, graph types, algorithm complexity, input file format, and graph features. On the basis of the social network mining aspects, the chapter provides a comparative study on five specialized tools—Weka, NetMiner 4, RapidMiner, KNIME, and R—with respect to the supported mining tasks, main functionality, acceptable input formats, output formats, and platform used.

Structured Self-Supervised Pretraining for Commonsense Knowledge Graph Completion

To develop commonsense-grounded NLP applications, a comprehensive and accurate commonsense knowledge graph (CKG) is needed. It is time-consuming to manually construct CKGs and many research efforts have been devoted to the automatic construction of CKGs. Previous approaches focus on generating concepts that have direct and obvious relationships with existing concepts and lack an capability to generate unobvious concepts. In this work, we aim to bridge this gap. We propose a general graph-to-paths pretraining framework that leverages high-order structures in CKGs to capture high-order relationships between concepts. We instantiate this general framework to four special cases: long path, path-to-path, router, and graph-node-path. Experiments on two datasets demonstrate the effectiveness of our methods. The code will be released via the public GitHub repository.