We revise our former definition of graph operations and correspondingly adapt the construction of graph term algebras. As a first contribution to a prospective research field, Universal Graph Algebra, we generalize some basic concepts and results fro...
In the modern era, mathematical modeling consisting of graph theoretic parameters or invariants applied to solve the problems existing in various disciplines of physical sciences like computer sciences, physics, and chemistry. Topological indices (TI...
A new family of graph operations based on multipartite graph with an arbitrary number of parts is defined and their applications are explored in this paper. The complete spectra of graphs derived from multipartite graphs are determined. Because the a...
A graph operator is a mapping
A chemical graph is an illustration of a chemical compound’s structural formula, where the edges indicate covalent bonding and the vertices depict atoms. In the study of (molecular) graphs, Zagreb indices and their variations are the most studi...
The resistance distance is a squared Euclidean metric on the vertices of a graph derived from the consideration of a graph as an electrical circuit. Its connection with the commute time of a random walker on the graph has made it particularly appeali...
A description of the 11 well-known uninodal planar nets is given by Cayley color graphs or alternative Cayley color graphs of plane groups. By applying methods from topological graph theory, the nets are derived from the bouquet
In this paper, we introduce the concepts of Harary Laplacian-energy-like for a simple undirected and connected graph G with order n. We also establish novel matrix results in this regard. Furthermore, by employing matrix order reduction techniques, w...
We bring together in one place some of the main results and applications from our recent work on quantum information theory, in which we have brought techniques from operator theory, operator algebras, and graph theory for the first time to investiga...
In this article, the consensus-related performances of the triplex multi-agent systems with star-related structures, which can be measured by the algebraic connectivity and network coherence, have been studied by the characterization of Laplacian spe...
Using equivalent transformations, complicated circuits in physics that need numerous mathematical operations to analyze can be broken down into simpler equivalent circuits. It is also possible to determine the number of spanning trees—graph fam...
We present a new combinatorial approach to the Ising model incorporating arbitrary bond weights on planar graphs. In contrast to existing methodologies, the exact free energy is expressed as the determinant of a set of ordered and disordered operator...
The security of traditional public key cryptography algorithms depends on the difficulty of the underlying mathematical problems. Asymmetric topological encryption is a graph-dependent encryption algorithm produced to resist attacks by quantum comput...
In this article, the performance indices on consensus problems for three-layered, multiagent systems are studied from the perspective of algebraic graph theory, where the indices can be used as a measurement of the system performance and refer to the...
Knowledge graph (KG) technology is a newly emerged knowledge representation method in the field of artificial intelligence. Knowledge graphs can form logical mappings from cluttered data and establish triadic relationships between entities. Accurate...
Some years ago, the harmonic polynomial was introduced to study the harmonic topological index. Here, using this polynomial, we obtain several properties of the harmonic index of many classical symmetric operations of graphs: Cartesian product, coron...
Rotating machinery serves as a critical component in various engineering systems, making accurate prediction of its Remaining Useful Life (RUL) essential for ensuring operational stability. To address the technical limitations of mainstream RUL predi...
A fault diagnosis method using bond graphs in an expert system is proposed for a reactor coolant system. Firstly, the time causality graph and the variable relationship graph are derived from the bond graph. Secondly, the fault signature matrix is ob...
Let X be a partitioned matrix and let B its equitable quotient matrix. Consider a simple, undirected, connected graph G of order n. In this paper, we employ a technique based on quotient matrices derived from block-partitioned structures to establish...
The complexity (number of spanning trees) in a finite graph
Mason’s gain formula can grow factorially because of growth in the enumeration of paths in a directed graph. Each of the (n − 2)! permutation of the intermediate vertices includes a path between input and output nodes. This paper presents...
This study presents a graph knowledge-enhanced iterated greedy algorithm that incorporates dual directional decoding strategies, disjunctive graphs, neighborhood structures, and a rapid evaluation method to demonstrate its superior performance for th...
In a peer-to-peer complex environment, information is permanently diffused. Such an environment can be modeled as a graph, where there are flows of information. The interest of such modeling is that (1) one can describe the exchanges through time fro...
In recent years, remarkable advancements have been achieved in hyperspectral unmixing (HU). Sparse unmixing, in which models mix pixels as linear combinations of endmembers and their corresponding fractional abundances, has become a dominant paradigm...
In a high-speed rail system, the driver repeatedly adjusts the train’s speed and traction while driving, causing a high level of energy consumption. This also leads to the instability of the train’s operation, affecting passengers’...
Topological relations form the backbone of qualitative spatial reasoning and, as such, play a paramount role in geographic information systems. Three decades of research have provided a proliferation of sets of qualitative topological relations in bo...
The multivariate Mittag–Leffler function is introduced and used to establish fractional calculus operators. It is shown that the fractional derivative and integral operators are bounded. Some fundamental characteristics of the new fractional op...
For random walks on a complex network, the configuration of a network that provides optimal or suboptimal navigation efficiency is meaningful research. It has been proven that a complete graph has the exact minimal mean hitting time, which grows line...
This work studies the first-order coherence of noisy multi-agent networks with multi-layered structures. The coherence, which is a sort of performance index of networks, can be seen as a sort of measurement for a system’s robustness. Graph oper...
Fault diagnosis in modern industrial and information systems is critical for ensuring equipment reliability and operational safety, but traditional methods have difficulty in effectively capturing spatiotemporal dependencies and fault-sensitive featu...
The extension of the concept of p-summability for linear operators to the context of Lipschitz operators on metric spaces has been extensively studied in recent years. This research primarily uses the linearization of the metric space M afforded by t...
In this work, we explore Wirtinger-type inequalities involving tempered Ψ-Caputo fractional derivatives by utilizing Taylor’s formula. We establish more general inequalities for the same operator in
We constructed a summation–integral type operator based on the latest research in the linear positive operators area. We establish some approximation properties for this new operator. We highlight the qualitative part of the presented operator;...
Although graph convolutional networks have found application in polarimetric synthetic aperture radar (PolSAR) image classification tasks, the available approaches cannot operate on multiple graphs, which hinders their potential to generalize effecti...
The study of networks and graphs carried out by topological measures performs a vital role in securing their hidden topologies. This strategy has been extremely used in biomedicine, cheminformatics and bioinformatics, where computations dependent on...
The current study is of interest when performing a useful extension of a crucial physical problem through a non-local singular fractional operator. We provide solutions that include three arbitrary parameters
We develop online graph learning algorithms from streaming network data. Our goal is to track the (possibly) time-varying network topology, and affect memory and computational savings by processing the data on-the-fly as they are acquired. The setup...
In this article, we derive the above and below bounds for parameterized-type inequalities using the Riemann–Liouville fractional integral operators and limited second derivative mappings. These established inequalities generalized the midpoint-...
Predicting wind speed over the ocean is difficult due to the unequal distribution of buoy stations and the occasional fluctuations in the wind field. This study proposes a dynamic graph embedding-based graph neural network—long short-term memor...
Unplanned dilution is a critical challenge in underground mining, directly affecting operating costs, resource recovery, stope stability and operational safety. This study presents an empirical–statistical framework that integrates the Mathews&...
Multi-sensor fault diagnosis, especially when using heterogeneous sensors, substantially enhances the accuracy of fault detection in asynchronous motors operating under high-interference conditions. A critical challenge in multi-sensor fault diagnosi...
A general lack of understanding pertaining to deep feedforward neural networks (DNNs) can be attributed partly to a lack of tools with which to analyze the composition of non-linear functions, and partly to a lack of mathematical models applicable to...
Three different fractional models of Oldroyd-B fluid are considered in this work. Blood is taken as a special example of Oldroyd-B fluid (base fluid) with the suspension of gold nanoparticles, making the solution a biomagnetic non-Newtonian nanofluid...
Ore dilution is a fundamental problem for the production process in underground mining operations. Especially in open stoping methods of underground mining, the continuous estimation, monitoring and treatment of instability issues is considered neces...
Operation rule plays an important role in the scientific management of hydropower reservoirs, because a scientifically sound operating rule can help operators make an approximately optimal decision with limited runoff prediction information. In past...
Simpson’s rule is a numerical method used for approximating the definite integral of a function. In this paper, by utilizing mappings whose second derivatives are bounded, we acquire the upper and lower bounds for the Simpson-type inequalities...
The fractional powers of generators for analytic operator semigroups are used for the proof of the existence and uniqueness of a solution of the Cauchy problem to a first order semilinear equation in a Banach space. Here, we use an analogous construc...
Grossman and Katz (five decades ago) suggested a new definition of differential and integral calculus which utilizes the multiplicative and division operator as compared to addition and subtraction. Multiplicative calculus is a vital part of applied...
The Kortweg–de Vries equations play an important role to model different physical phenomena in nature. In this research article, we have investigated the analytical solution to system of nonlinear fractional Kortweg–de Vries, partial diff...
Typhoon disasters not only trigger secondary disasters, such as rainstorms and flooding, but also bring many negative impacts on the normal operation of urban infrastructure and the safety of people’s lives and property. In order to effectively...
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