## 1 Introduction  
Wireless sensor networks (WSNs) are formed by a large collection of power-conscious wireless-capable sensors without the support of pre-existing infrastructure, possibly by unplanned deployment. With the sheer number of sensor nodes, their unattended deployment and hostile environment very often preclude reliance on physical configuration or physical topology. It is, therefore, often necessary to depend on the logical topology. The logical topology of a wireless sensor network is formed by the communication graph of the network. A communication graph of a WSN is an undirected graph \(G=(V,E)\) where \(V\) denotes the sensors deployed, and \(E\) denotes the available communication links among the sensor nodes. As logical topology inherently defines the type of routing paths, indicates whether to use broadcast or unicast, and determines the sizes and types of packets and other overheads, choosing the right topology helps to reduce the amount of communication needed for a particular problem. Thus energy can be saved. An efficient topology, which ensures that neighbours are at a minimal distance, reduces the probability of message being lost between sensors. A topology can also reduce the radio interference, thus reducing the waiting time for sensors to transmit data [1, 2, 3]. Moreover, topology facilitates data aggregation, which greatly reduces the amount of processing cycles and energy, resulting in a longer lifetime for the network [4, 5]. In addition, topology inherently defines the size of a group, how to manage new members in a group, and how to deal with members who have left the group. With the awareness of the underlying network topology, more efficient routing or broadcasting schemes can be achieved. Furthermore, the network topology in WSNs can be changed by varying the nodes' transmitting ranges and also by adjusting the wake/sleep schedule of the nodes [6, 7]. Therefore, more energy can be saved if the network topology is maintained in an optimal manner. Additionally, much research has taken place to justify the performance of different logical topologies [8, 9, 10, 11]. Chain oriented topology has been identified as being more promising than other topologies of WSNs [12, 13, 14, 15, 16, 17, 18]. Chain oriented topologies minimise many of the constraints of WSNs. For example, energy consumptions by the sensor nodes can be greatly reduced by the chain oriented topology [19, 20, 21, 22]. For data fusion/aggregation, chain oriented topology offers substantial advantages due to the logical structure of the sensor nodes [23, 24]. It is also possible to obtain collision-free transmissions using a chain oriented topology [25]. Other WSNs requirements, such as connectivity, robustness, scalability, responsiveness, and reliability, can also be enhanced by chain oriented topologies. To achieve the abovementioned outcomes, the careful design of chain oriented topology is essential. Designing a logical topology for WSNs needs to be considered from different perspectives, namely: (i) resource oriented considerations, such as energy consumption and time requirement; (ii) networking related considerations, such as connectivity, robustness, and reliability; (iii) data centric considerations, such as data collection strategies and data aggregation facilities; (iv) architecture oriented considerations, such as scalability, task orientation, and light weighting; and (v) Network management considerations, such as fault detection and performance management. The drawbacks of chain oriented topologies, such as latency, also need to be considered. In this paper, we propose a variant of chain oriented logical topology. The main aim of this study is to design a logical topology, so that the proposed topology retains the advantages of the chain oriented topologies, and at the same time, overcomes the problems of the chain oriented topology. In designing the proposed logical topology, we considered all the aspects discussed above.