33 Results Found

The field of indices has been explored and advanced by various researchers for different purposes. One purpose is the optimization of indices in various problems. In this work, the general power-sum connectivity index is considered. The general power...

If G is a graph, its Laplacian is the difference between the diagonal matrix of its vertex degrees and its adjacency matrix. A one-edge connection of two graphs $G_1$ and $G_2$ is a graph $G=G_1{\odot }_{uv}{G}_2$ with $V(G$...

In a certain class of graphs, a graph is called minimizing if the least eigenvalue of its adjacency matrix attains the minimum. A connected graph containing two or three cycles is called a bicyclic graph if its number of edges is equal to its number...

Let G be a simple connected graph with edge set $E\left(G\right)$ and vertex set $V\left(G\right)$. The weighted Mostar index of a graph G is defined as $w^{+}Mo\left(G\right)={\displaystyle \sum _{e=uv\in E\left(G\right)}}(d_G\left(u\right)+d_G\left(v\right))|n_u\left(e\right)-n_v\left(e\right)|$, where $n_u\left(e\right)$ denotes the number of vertices closer to u than to...

For a connected graph G, let $D^L\left(G\right)$ be its distance Laplacian matrix and ${\lambda }_1\left(G\right)\ge {\lambda }_2\left(G\right)\ge \dots \ge {\lambda }_{n-1}\left(G\right)>{\lambda }_n\left(G\right)=0$ be its $D^L$ eigenvalues. The $D^L$ energy of G is defined as $DLE\left(G\right)={\sum }_{i=1}^n\left|{\lambda }_i\left(G\right)-{\displaystyle \frac{2W\left(G\right)}{n}}\right|$,...

Shared bicycles provide a green, environmentally friendly, and healthy mode of transportation that effectively addresses the “final mile” problem in urban travel. However, the uneven distribution of bicycles and the imbalance of user dema...

A connected graph with p vertices and q edges satisfying $q=p+1$ is referred to as a bicyclic graph. This paper is concerned with an optimal study of the BID (bond incident degree) indices of fixed-size bicyclic graphs with a given matching number. Her...

The distance $d(v_a,v_b)$ between two vertices of a simple connected graph G is the length of the shortest path between $v_a$ and $v_b$. Vertices $v_a,v_b$ of G are considered to be resolved by a vertex v if $d(v_a,v)\ne d(v_b,v)$. An ordered set $W=\{v_1,v_2,v_3,\dots ,$...

Let G be a connected graph; the edge Mostar index $M{o}_e\left(G\right)$ of G is defined as ${\displaystyle M{o}_e\left(G\right)=\sum _{e=uv\in E\left(G\right)}|m_u\left(e\right)-m_v\left(e\right)|,}$ where $m_u\left(e\right)$ and $m_v\left(e\right)$ denote the number of edges in G that are closer to vertex u than to vertex v and the number of edges that...

The field related to indices was developed by researchers for various purposes. Optimization is one of the purposes used by researchers in different situations. In this article, a generalized Sombor index is considered. This work is related to the id...

The topological index (TI), sometimes referred to as the connectivity index, is a molecular descriptor calculated based on the molecular graph of a chemical compound. Topological indices (TIs) are numeric parameters of a graph used to characterize it...

We present lower and upper bounds on the general multiplicative Zagreb indices for bicyclic graphs of a given order and number of pendant vertices. Then, we generalize our methods and obtain bounds for the general multiplicative Zagreb indices of tri...

Several topological indices are possibly the most widely applied graph-based molecular structure descriptors in chemistry and pharmacology. The capacity of topological indices to discriminate is a crucial component of their study. In light of this, t...

Degree sequence measurements on graphs have attracted a lot of research interest in recent decades. Multiplying the degrees of adjacent vertices in graph $\Omega$ provides the multiplicative first Zagreb index of a graph. In the context of graph theor...

Graph polynomials is one of the important research directions in mathematical chemistry. The coefficients of some graph polynomials, such as matching polynomial and permanental polynomial, are related to structural properties of graphs. The Hosoya in...

For a (molecular) graph G, the extended adjacency index $EA\left(G\right)$ is defined as Equation (1). In this paper we introduce some graph transformations which increase or decrease the extended adjacency ( $EA$ ) index. Also, we obtain the ext...

Understanding the regularity and determinants of mobility is indispensable for the reasonable deployment of shared bicycles and urban planning. A spatial interaction network covering streets in Beijing’s six main districts, using bike sharing d...

A double-star $S_{q_1,q_2}$ is the graph consisting of the union of two stars, $K_{1,q_1}$ and $K_{1,q_2}$, together with an edge joining their centers. The spectrum for $S_{q_1,q_2}$-designs, i.e., the set of all the $n\in \mathbb{N}$ such that an $S_{q_1,q_2}$-design of the order n exists,...

Facing the Bicycle Rebalancing Problem (BRP), we established a Rebalancing Incentive System (BRIS). In BRIS, the bicycle operator proposes the method of financial compensation to encourage cylclists to detour some specific stations where the number o...

The definition of a Detour–Harary index is $\omega H(G)=\frac{1}{2}{\sum }_{u,v\in V(G)}$ $\frac{1}{l(u,v|G)}$ , where G is a simple and connected graph, and $l(u,v|G)$ is equal to the length of the longest p...

The study of the maximum and minimal characteristics of graphs is the focus of the significant field of mathematics known as extreme graph theory. Finding the biggest or smallest graphs that meet specified criteria is the main goal of this discipline...

Graham and Pollack in 1971 presented applications of eigenvalues of the distance matrix in addressing problems in data communication systems. Spectral graph theory employs tools from linear algebra to retrieve the properties of a graph from the spect...

A topological index is a number that is connected to a chemical composition in order to correlate a substance’s chemical makeup with different physical characteristics, chemical reactivity, or biological activity. It is common to model drugs an...

With the rapid development of sharing bicycles, unreasonable dispatching methods are likely to cause a series of issues, such as resource waste and traffic congestion in the city. In this paper, a new dynamic scheduling method is proposed, named Tri-...

Bicycle sharing systems (BSSs) have established a new shared-economy mobility model. After a rapid growth they are evolving into a fully-functional mobile sensor platform for cities. The viability of BSSs is floored by their operational costs, mainly...

Commercially available Pt screen printed electrodes (SPEs) have been employed as possible electrode materials for methylamine (MA) and hydrogen chloride (HCl) gas detection. The room temperature ionic liquid (RTIL) 1-ethyl-3-methylimidazolium bis(tr...

Electric cargo bicycles have become a popular mode of transport for last-mile goods deliveries under conditions of restricted traffic in urban areas. The indispensable elements of the cargo bike delivery systems are loading hubs: they serve as interm...

Parks provide essential services to urban dwellers, but the global COVID-19 pandemic significantly disrupted park usage. Despite this, little is known about the adaptation of visiting behaviors by the public and how visitation patterns vary across di...

The article describes sustainable transport principles and guides that can lead cities towards a more efficient transportation network. The authors also show good practice used in different urban areas, such as London and Copenhagen. Furthermore, Vil...

Jasmonates show great potential in sustainable agriculture due to their various roles in natural mechanisms of plant defense, and because they are non-toxic, non-mutagenic, and easily metabolized. The aim of the study was to explore structure–a...

During public health emergencies, studying the travel characteristics and influencing factors of shared bicycles during different time periods on weekdays can provide valuable insights for urban transportation planning and offer recommendations for b...

This article presents an interaction-aware motion planning framework that integrates a graph neural network (GNN) based multi-modal trajectory predictor with a model predictive control (MPC) based planner. Unlike past studies that predict a single fu...

This paper deals with a variant of the multifacility location-routing problem in urban areas. The distribution network is modelled by an undirected graph, in which the nodes are split into a set of pickup-delivery stations, a depot, and a set of cust...