67 Results Found

The number of subtrees, or simply the subtree number, is one of the most studied counting-based graph invariants that has applications in many interdisciplinary fields such as phylogenetic reconstruction. Motivated from the study of graph surgeries o...

Consider G to be a simple graph with n vertices and m edges, and $L\left(G\right)$ to be a Laplacian matrix with Laplacian eigenvalues of ${\mu }_1,{\mu }_2,\dots ,{\mu }_n=zero$. Write $S_k\left(G\right)={\sum }_{i=1}^k{\mu }_i$ as the sum of the k-largest Laplacian eigenvalues of G, where $k\&i$...

The BC-subtree (a subtree in which any two leaves are at even distance apart) number index is the total number of non-empty BC-subtrees of a graph, and is defined as a counting-based topological index that incorporates the leaf distance constraint. I...

Stanley depth is a geometric invariant of the module and is related to an algebraic invariant called depth of the module. We compute Stanley depth of the quotient of edge ideals associated with some familiar families of wheel-related graphs. In parti...

Let G be a graph with n vertices and m edges. A vertex magic total labeling of G is a bijection $f:V\left(G\right)\cup E\left(G\right)\to \{1,2,\dots ,n+m\}$ such that, for each vertex $u\in V\left(G\right)$, the sum of the label of u and the labels of all edges incident to u is equ...

A graph, $G=(V,E)$, is edge odd graceful if it possesses edge odd graceful labeling. This labeling is defined as a bijection $g:E\left(G\right)\to \{1,3,\dots ,2m-1\}$, from which an injective transformation is derived, $g^{*}:V\left(G\right)\to \{1,2,3,\dots ,2m\&minus$...

The studies in epidemic-like processes have drawn much attention for the last decades. Structural or dynamical heterogeneity has been reported to have great impact on the statistical properties of the epidemic dynamics. In this work, we investigate t...

A k-labeling from the vertex set of a simple graph $G=(V,E)$ to a set of integers $\{1,2,\dots ,k\}$ is defined to be a modular edge irregular if, for every couple of distinct edges, their modular edge weights are distinct. The modular edge weight is the...

A graph’s edge labeling involves the allocation of symbols (colors or numbers) to the edges of a graph governed by specific criteria. Such labeling of a graph G with order n and size m is named edge odd graceful if there is a bijective map $\mathrm{\&phi}$...

Let $G=(V,E)$ be a connected graph with $\left|V\right|=n$ and $\left|E\right|=m$. A bijection $f:V\left(G\right)\cup E\left(G\right)\to \{1,2,\cdots ,n+m\}$ is called local antimagic total labeling if, for any two adjacent vertices u and v, ${\omega }_t\left(u\right)\ne {\omega }_t\left(v\right)$, where ${\omega }_t\left(u\right)=f\left(u\right)+{\sum }_{e\&is}$...

For an undirected graph G, a zero-sum flow is an assignment of nonzero integer weights to the edges such that each vertex has a zero-sum, namely the sum of all incident edge weights with each vertex is zero. This concept is an undirected analog of no...

Energies of molecular graphs have various applications in chemistry, polymerization, computer networking and pharmacy. In this paper, we give general closed forms of distance and adjacency energies of generalized wheel networks $W_{n,m}$ . C...

The crossing number of a graph is a significant measure that indicates the complexity of the graph and the difficulty of visualizing it. In this paper, we examine the crossing numbers of join products involving the complete graph $K_5$ with discrete gra...

A topological index is a number related to the atomic index that allows quantitative structure–action/property/toxicity connections. All the more vital topological indices correspond to certain physico-concoction properties like breaking point,...

Synchronizing a network of robots in consensus is an important task for cooperative work. Detecting faults in a network of robots in consensus is a much more important task. In considering a formation of Wheeled Mobile Robots (WMRs) in a master&ndash...

The problem of quantifying the vulnerability of graphs has received much attention nowadays, especially in the field of computer or communication networks. In a communication network, the vulnerability measures the resistance of the network to disrup...

The primary objective of this study is the computation of the matching polynomials of a number of symmetric, semisymmetric, double group graphs, and solids in third and higher dimensions. Such computations of matching polynomials are extremely challe...

This paper presents the application of the concepts and approaches of linear graph (LG) theory in the modeling and simulation of a four-wheel skid-steer mobile robotic system. An LG representation of the system is proposed, and the accompanying state...

This research introduces two novel topological indices, the entire Albertson index and the entire sigma index, as quantitative measures of molecular irregularity. The indices are defined by precise mathematical formulas and their behavior is analyzed...

Complexity (number of spanning trees) is an essential and significant component in the design of communication networks (graphs). To ensure strong resistance and stiffness and to enhance the probability of a connection between two vertices, improveme...

Providing mobile robots with autonomous capabilities is advantageous. It allows one to dispense with the intervention of human operators, which may prove beneficial in economic and safety terms. Autonomy requires, in most cases, the use of path plann...

Let G = (V, E) be a connected graph and d(u, v) denote the distance between the vertices u and v in G. A set of vertices W resolves a graph G if every vertex is uniquely determined by its vector of distances to the vertices in W. A metric dimension o...

In graph theory, a graph is given names—generally a whole number—to edges, vertices, or both in a chart. Formally, given a graph $G=(V,E)$ , a vertex naming is a capacity from V to an arrangement of marks. A diagram with such a...

In this paper, motivated by the recently introduced topological indices—the Sombor index, Sombor coindex, and Lanzhou index, we define a new index—the Lanzhou coindex of a graph. Furthermore, we investigate the Sombor index (coindex) and...

This paper presents a method for the multi-criteria classification of data in terms of identifying pneumatic wheel imbalance on the basis of vehicle body vibrations in normal operation conditions. The paper uses an expert system based on search graph...

It is easily observed that the vertices of a simple graph cannot have pairwise distinct degrees. This means that no simple graph of the order of at least two is, in this way, irregular. However, a multigraph can be irregular. Chartrand et al., in 198...

In this paper, we introduce the notion of g-convex weight sequence (gcws) for connected graphs based on the concept of g-convexity and g-weight. g-weight is a natural generalization of the notion of branch weight for trees. We investigate the various...

Topological indices (molecular descriptors) are numerical values of a chemical structure and represented by a graph. Molecular descriptors are used in QSPR/QSAR modeling to determine a chemical structure’s physical, biological, and chemical pro...

Let $G=(V,E)$ be a graph with vertex set V and edge set E. A local antimagic total vertex coloring f of a graph G with vertex-set V and edge-set E is an injective map from $V\cup E$ to $\{1,2,\dots ,|V|+|E\left|\right\}$ such that if for each $uv\in E\left(G\right)$ then $w\left(u\right)\&n$...

This article deals with the influence of the elastic-damping properties (energy losses) of tired wheels on the results of the evaluation of the technical condition (dynamic properties) of automotive suspensions carried out on the diagnostic line. The...

The crossing number $\mathrm{cr}\left(G\right)$ of a graph G is the minimum number of edge crossings over all drawings of G in the plane. The main aim of this paper is to give the crossing numbers of the join products $G^{*}+P_n$ and $G^{*}+C_n$ for the connected graph $G^{*}$ obtained by...

In this paper, we used the permutation group together with the concept of cordiality in graph theory to introduce a new method of labeling. This construed permuted cordial labeling can be applied to all paths, cycles, fans and wheel graphs. Moreover,...

In this paper we used the cubic roots of unit group together with the concept of cordiality in graph theory to introduce a new method of labeling, this construed cubic cordial labeling can be applied to all paths, cycles, fans and wheel graphs. Moreo...

Graph coloring is one of the most studied problems in graph theory due to its important applications in task scheduling and pattern recognition. The main aim of the problem is to assign colors to the elements of a graph such as vertices and/or edges...

Robustness in networks plays a vital role in mitigating the effects of failures caused by nodes or links, which can disrupt essential services. Among the various vulnerability parameters in graph theory, such as connectivity and integrity, their appl...

This article presents a design and performance analysis of an Electronic Differential (ED) system designed for Light Electric Vehicles (LEVs). We have developed a test tricycle vehicle with one front steering wheel and two rear fixed units in the sam...

This article considers the methods of calculating the number of operations for the fine grinding of cold rolling rolls which allows one to ensure the least labor-intensive processing of the part. Based on the analysis of the patterns in the operation...

Graph theory is a crucial branch of mathematics in fields like network analysis, molecular chemistry, and computer science, where it models complex relationships and structures. Many indices are used to capture the specific nuances in these structure...

In this paper, we present an active fault-tolerant, vehicle motion control, based on the multi-agent approach for a four-wheel independent steering system. This improves handling stability and active safety of the vehicle in the case of actuator faul...

This paper proposes a method to solve the problem of localization and mapping of a two-wheeled inverted pendulum (TWIP) robot on approximately flat ground using a Lidar–IMU–Odometer system. When TWIP is in motion, it is constrained by the...

To achieve optimal controllability in a dual steering tractor (a four-wheel, iso-diametric tractor equipped with a dual-hydraulic steering system), this study proposes a coordinated approach that combines experimental testing (using a special agricul...

The presence of contaminants influences braking efficiency in the railway system because it alters the adhesion at the wheel–rail interface. It is essential to study this phenomenon, as contaminants reduce the friction between wheels and rails,...

Analyzing events in dynamic environments poses a fundamental challenge in the development of intelligent agents and robots capable of interacting with humans. Current approaches predominantly rely on visual–text models; however, these methods o...

In this paper, for an Low-Earth Orbit (LEO) satellite network with inter-satellite links, a routing optimization method is developed in the case of stochastic link failure. First, a discrete-time strategy is used for the satellite network to acquire...

The problem that it is difficult to balance vehicle stability and economy at the same time under the starting steering condition of a four-wheel independent drive electric vehicle (4WIDEV) is addressed. In this paper, we propose a coordinated optimal...

A vehicle with a four-channel anti-lock braking system (ABS) has poor safety and stability when braking on a low-adhesion road or off-road. In view of this situation, this paper proposes a multi-objective optimization coordinated control method for A...

Underground mining machines, such as wheel-tyre drilling rigs, are articulated and equipped with booms that project far beyond the undercarriage. Such a structure makes these machines prone to losing stability. Hence, it is necessary to analyse the d...

This paper addresses a recursive adaptive anti-lock braking (AB) control design problem for electro-hydraulic brake (EHB) systems subject to unknown tire–road-friction coefficients and disturbances. Compared with the relevant literature, the pr...

The health status of the momentum wheel is vital for a satellite. Recently, research on anomaly detection for satellites has become more and more extensive. Previous research mostly required simulation models for key components. However, the physical...

Air cycle systems (ACSs) are primarily used in aircraft environmental control systems (ECSs) to provide a suitable cabin temperature and pressure environment for passengers and avionics. It comprises heat exchangers, compressors, turbines, water sepa...