Locating the source of diffusion in complex networks is an exciting but challenging task. It is critical for preventing and controlling the epidemic risks. Source localization has been studied under many feasible models. In this paper, we discuss the localization problem in Kayak paddle graphs [Formula: see text] for [Formula: see text] and [Formula: see text] by computing edge version of metric and double metric dimensions.

The field of graph theory is extensively used to investigate structure models in biology, computer programming, chemistry, and combinatorial optimization. In order to work with the chemical structure, chemists require a mathematical form of the compound. The chemical structure can be depicted using nodes (which represent the atom) and links (which represent the many types of bonds). As a result, a graph theoretic explanation of this problem is to give representations for the nodes of a graph such that different nodes have unique representations. This graph theoretic study is referred to as the metric dimension. In this article, we have computed the edge version of the metric dimension and doubly resolving sets for the family of cycle with chord C n t for n ≥ 6 and 2 ≤ t ≤ ⌊ n / 2 ⌋ .

A source detection problem in complex networks has been studied widely. Source localization has much importance in order to model many real-world phenomena, for instance, spreading of a virus in a computer network, epidemics in human beings, and rumor spreading on the internet. A source localization problem is to identify a node in the network that gives the best description of the observed diffusion. For this purpose, we select a subset of nodes with least size such that the source can be uniquely located. This is equivalent to find the minimal doubly resolving set of a network. In this article, we have computed the double metric dimension of convex polytopes R n and Q n by describing their minimal doubly resolving sets.

Nowadays, the study of source localization in complex networks is a critical issue. Localization of the source has been investigated using a variety of feasible models. To identify the source of a network’s diffusion, it is necessary to find a vertex from which the observed diffusion spreads. Detecting the source of a virus in a network is equivalent to finding the minimal doubly resolving set (MDRS) in a network. This paper calculates the doubly resolving sets (DRSs) for certain convex polytope structures to calculate their double metric dimension (DMD). It is concluded that the cardinality of MDRSs for these convex polytopes is finite and constant.

Locating the sources of information spreading in networks including tracking down the origins of epidemics, rumors in social networks, and online computer viruses, has a wide range of applications. In many situations, identifying where an epidemic started, or which node in a network served as the source, is crucial. But it can be difficult to determine the root of an outbreak, especially when data are scarce and noisy. The goal is to find the source of the infection by analysing data provided by only a limited number of observers, such as nodes that can indicate when and where they are infected. Our goal is to investigate where the least number of observers should be placed, which is similar to how to figure out the minimal doubly resolving sets in the network. In this paper, we calculate the double metric dimension of chordal ring networks C R n 1,3,5 by describing their minimal doubly resolving sets.