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 >

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

Intelligent Automation & Soft Computing, Vol.36, No.2, pp. 2349-2361, 2023, DOI:10.32604/iasc.2023.032930

Abstract In this paper, we consider the NP-hard problem of finding the minimum connected 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 B of G is connected if the subgraph induced by B is a nontrivial connected subgraph of G. The cardinality of the minimal resolving set is the metric dimension of G and the cardinality of minimum connected resolving set is the connected metric dimension of G. The problem is solved heuristically… 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 >