Wiener Index of Extended Fibonacci Cubes

The series of Extended Fibonacci cubes defined in terms of Fibonacci strings are classes of incomplete hypercubes. The Wiener index of a network, also known as the transmission of a network, is the sum of distances between all pairs of vertices in the network. It provides the average distance between any two nodes of the network. An embedding of a graph [Formula: see text] into a graph [Formula: see text] is a one-to-one mapping of [Formula: see text] into [Formula: see text]. Wirelength is a widely studied embedding parameter. In this paper, we determine the Wiener index of all cubes in the series of Extended Fibonacci cubes. We also find the wirelength of embedding a complete graph with a deleted edge onto the Extended Fibonacci cubes.