Basma Mohamed^1,*, Linda Mohaisen², Mohammed Amin¹

Intelligent Automation & Soft Computing, Vol.38, No.1, pp. 19-34, 2023, DOI:10.32604/iasc.2023.031947

Abstract In this paper, we consider the NP-hard problem of finding the minimum dominant resolving set of graphs. A vertex set B of a connected graph G resolves G if every vertex of G is uniquely identified by its vector of distances to the vertices in B. A resolving set is dominating if every vertex of G that does not belong to B is a neighbor to some vertices in B. The dominant metric dimension of G is the cardinality number of the minimum dominant resolving set. The dominant metric dimension is computed by a binary version of the Archimedes optimization… More >

Ali N. A. Koam¹, Ali Ahmad^2,*, Maryam Salem Alatawi³, Muhammad Azeem⁴, Muhammad Faisal Nadeem⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.3, pp. 3011-3024, 2023, DOI:10.32604/cmes.2023.024764

Abstract The Metric of a graph plays an essential role in the arrangement of different dimensional structures and finding their basis in various terms. The metric dimension of a graph is the selection of the minimum possible number of vertices so that each vertex of the graph is distinctively defined by its vector of distances to the set of selected vertices. This set of selected vertices is known as the metric basis of a graph. In applied mathematics or computer science, the topic of metric basis is considered as locating number or locating set, and it has applications in robot navigation… More >

Xiujun Zhang¹, Muhammad Salman², Anam Rani³, Rashna Tanveer², Usman Ali^3,*, Zehui Shao⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.1, pp. 883-899, 2023, DOI:10.32604/cmes.2023.025162

Abstract The distance between two vertices u and v in a connected graph G is the number of edges lying in a shortest path (geodesic) between them. A vertex x of G performs the metric identification for a pair (u, v) of vertices in G if and only if the equality between the distances of u and v with x implies that u = v (That is, the distance between u and x is different from the distance between v and x). The minimum number of vertices performing the metric identification for every pair of vertices in G defines the metric… More >

Dalal Awadh Alrowaili¹, Mohsin Raza², Muhammad Javaid^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.3, pp. 2697-2713, 2023, DOI:10.32604/cmes.2023.023017

Abstract The problem of investigating the minimum set of landmarks consisting of auto-machines (Robots) in a connected network is studied with the concept of location number or metric dimension of this network. In this paper, we study the latest type of metric dimension called as local fractional metric dimension (LFMD) and find its upper bounds for generalized Petersen networks GP(n, 3), where n ≥ 7. For n ≥ 9. The limiting values of LFMD for GP(n, 3) are also obtained as 1 (bounded) if n approaches to infinity. More >

Muhammad Ahmad¹, Fahd Jarad^2,3,*, Zohaib Zahid¹, Imran Siddique¹

CMES-Computer Modeling in Engineering & Sciences, Vol.135, No.3, pp. 2681-2696, 2023, DOI:10.32604/cmes.2023.022819

Abstract The doubly resolving sets are a natural tool to identify where diffusion occurs in a complicated network. Many real-world phenomena, such as rumour spreading on social networks, the spread of infectious diseases, and the spread of the virus on the internet, may be modelled using information diffusion in networks. It is obviously impractical to monitor every node due to cost and overhead limits because there are too many nodes in the network, some of which may be unable or unwilling to send information about their state. As a result, the source localization problem is to find the number of nodes… More >

Sohail Abbas¹, Zahid Raza², Nida Siddiqui², Faheem Khan³, Taegkeun Whangbo^3,*

CMC-Computers, Materials & Continua, Vol.71, No.2, pp. 2683-2695, 2022, DOI:10.32604/cmc.2022.023003

Abstract Wireless Sensor Network (WSN) is considered to be one of the fundamental technologies employed in the Internet of things (IoT); hence, enabling diverse applications for carrying out real-time observations. Robot navigation in such networks was the main motivation for the introduction of the concept of landmarks. A robot can identify its own location by sending signals to obtain the distances between itself and the landmarks. Considering networks to be a type of graph, this concept was redefined as metric dimension of a graph which is the minimum number of nodes needed to identify all the nodes of the graph. This… More >

Muhammad Imran^1,*, Ali Ahmad², Muhammad Azeem³, Kashif Elahi⁴

CMC-Computers, Materials & Continua, Vol.71, No.1, pp. 2053-2071, 2022, DOI:10.32604/cmc.2022.022064

Abstract Silica has three major varieties of crystalline. Quartz is the main and abundant ingredient in the crust of our earth. While other varieties are formed by the heating of quartz. Silica quartz is a rich chemical structure containing enormous properties. Any chemical network or structure can be transformed into a graph, where atoms become vertices and the bonds are converted to edges, between vertices. This makes a complex network easy to visualize to work on it. There are many concepts to work on chemical structures in terms of graph theory but the resolvability parameters of a graph are quite advance… More >

Tantan Zhu^*, Yao Li

CMES-Computer Modeling in Engineering & Sciences, Vol.126, No.2, pp. 457-477, 2021, DOI:10.32604/cmes.2021.014284

Abstract Punch shear tests have been widely used to determine rock shear mechanical properties but without a standard sample geometric dimension suggestion. To investigate the impacts of sample geometric dimensions on shear behaviors in a punch shear test, simulations using Particle Flow Code were carried out. The effects of three geometric dimensions (i.e., disk diameter, ratio of shear surface diameter to disk diameter, and ratio of disk height to shear surface diameter) were discussed. Variations of shear strength, shear stiffness, and shear dilatancy angles were studied, and the fracture processes and patterns of samples were investigated. Then, normal stress on the… More >