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For many wireless ad-hoc network (WANET) applications, including wireless sensor, robotic, and flying ad-hoc networks, area coverage is a major challenge. This challenge, which may include the number of required nodes, cumulative energy consumption, or total distance travelled, involves covering the largest possible area with the least cost. Whatever the scenario and cost functions, efficiently deploying the nodes throughout their entire missions is an important factor. For larger networks, this can best be performed using proper topology formations that are essentially designated geometric graph patterns. As a network topology formation and node deployment strategy, this study presents a unique tree-formed geometric graph pattern. With any given number of nodes, it guarantees the maximum possible combined area coverage. Considering its graph theory and Euclidean characteristics, the pattern is then described as both algebraic and algorithmic relations. The formation is remarkably scalable because it may include an unlimited number of nodes while ensuring connectivity in a tree topology. In addition to presenting a breakdown of multiple features and attributes, including symmetry and fractality, we will make a comparative analysis with six known regular lattices and a line formation. Our analyses then show that MAX-Tree covers up to twice as much area compared to all other regular lattices of the same node cardinalities while being more robust and reliable than a line formation. MAX-Tree can be extremely beneficial for drone networks, smart industry and agriculture applications, ocean-bed monitoring systems, and many other WANET scenarios. [ABSTRACT FROM AUTHOR]

The Space today has considerable surge in distributed network of small satellites to meet the imperative demand of both commercial and scientific applications (Selva and Krejci in Acta Astronaut 74:50–68, 2012). As the complexity of the design and launch of large satellites is high , the need of distributed networking is gaining lot of interest in space domain as well. Thus single large satellite is replaced by many, small satellite that collaboratively work to perform the same functionality of single large satellite forming Space Based Wireless Sensor Network (SBWSN). The SBWSN are dynamically decoupled network as each satellite, orbits in its own path and the positioned with considerable distance between them. Stability of network with respect to formation flying to accomplish the task by collaboration is quite essential. In this paper, we develop the stability criteria in small satellite network using graph theory, covariant derivatives and linear algebra to ensure distributed processing and communication, required to accomplish the mission task. [ABSTRACT FROM AUTHOR]

The satellite network is one of the major source of information and these days small satellites are gaining lot of focus. The group of small satellites form a distributed network that work collaboratively to accomplish the mission task. These networks are very similar to the terrestrial wireless sensor network in terms of restricted resources and constrained capabilities. Sometimes, network of small satellites is also called as space based wireless sensor network (SBWSN). In any distributed network, topology formation and its control plays a significant role. This is true for SBWSN also. The topology in SBWSN decides the area of coverage (field of view), time of coverage, data gathered and data transmitted to ground station. The proposed topology is a distributed network of small satellites formed by trivalent, toroidal and spherical polyhedron graph forming a fullerene, which is called as polygon based network topology (PBNT). It comprises of both pentagonal (Fp) and hexagonal (Fh) faces with K regular graphs such that K ≥ 3 with genus equal to 1. It also satisfies Eulers formula with n vertices. The fullerene comprises of simple rings and each of this ring forms the cluster. Each cluster is further represented as a triangular grid, that is linearly convex or non-linear, with K-connected graph along with Hamiltonian extendible cycle. The nodes/satellites on the triangular grid represent sensing nodes (low capability nodes/satellites), while the vertices of the ring are sink nodes (higher capability nodes/satellites). In this work, the topology is formed by small satellites (pico or nano satellites). In the proposed topology formation, the network is considered as virtual network with logical neighbours forming the cluster. Each node in the cluster covers a particular swath for a particular time interval based on the mission payload and on the p3 tiling. In the simulation, we consider n small satellites being placed in low earth orbit (LEO), (where n ranges from 3 to 150). The performance enhancements are seen during simulation in the following parameters, (1) Coverage Area: The coverage area increases as multiple satellites have different field of view at different times. (2) Reduces Gaps:The proposed distributed network also minimises uncovered areas as multiple satellites cover the target location at different time stamp which is not possible by a single large satellite. (3) Increase in Data Throughput: Each satellite in the network transmits data, when it is at perigee. The data throughput of the network increases, as data is transmitted by multiple satellites. Therefore, the throughput is increased by n-fold. (4) Continuous Connectivity: The data captured by one satellite in the network is made available to other using multi-hop communication. Thus the proposed topology also increases the continuous connectivity between satellites and also with the ground station. (5) Increases lifetime and Network Reliability: The SBWSN accomplishes its mission task even when one/more satellites encounters functional failure. The satellites in the network can reconfigure themselves and continue the mission task. Thus SBWSN also reduces the risk of mission failure and ensures mission reliability. Due to reconfiguration the lifetime of the network is also increased. The proposed topology is used for small satellites (specially nano and pico satellites) network, which permit the single board satellite weighing less than 10 kg (Pico satellite less than 1 kg and nano satellites less than 10 kg). The advantage of these small satellites network over single large satellite is low cost and reduced development time, as it uses commercially of the shelf (COTS) components. In this paper, we propose network architecture formed by the spherically embedded clusters formed by polyhedron. The vertices of polyhedron have both pentagonal (Fp) and hexagonal (Fh) faces with K regular graphs such that K ≥ 3, with genus equal to 1. The vertices of these polyhedron form the sink nodes and the other nodes are sensing nodes. Here satellites and nodes are interchangeably used. Sensing nodes are used for data gathering (pico/nano), while sink nodes are higher capability nodes which perform computational extensive operations in the network (nano or macro satellites). The sensing and sink nodes transmit data to the ground station when they are at perigee. The main objective of the proposed work is, technology demonstration of low cost, distributed small satellites network for earth observations replacing single huge satellite. [ABSTRACT FROM AUTHOR]