Locating Number of Biswapped Networks

Abstract

A biswapped network is an interconnection network in multiprocessor systems. These are networks of devices or processors and connections of these devices or processors. Here network can be expressed in the form of a graph. Devices or processors represent vertices, and the connection of devices or processors represents edges. The subset of the nodes set is called the resolving set if all the representations or codes are different w.r.t. this subset gives the information about the complete network. The minimum cardinality of the resolving set is called the locating number. In this article, we find the locating number of biswapped interconnection networks. In this paper, We compute the exact values of locating numbers for biswapped networks generated by different families of underlying basis networks like path, cycle, power of path, and complete. We have also given the bounds of locating number of any biswapped network generated by any underlying basis network that consists of its clusters.