The Kirchhoff indexes of some composite networks

In electric circuit theory, it is of great interest to compute the effective resistance between any pair of vertices of a network, as well as the Kirchhoff index. During the past decade these parameters have been applied in organic chemistry as natural structural indexes different from the usual ones in order to achieve an improvement in the discrimination between different molecules that have similar structural behaviours. This new application has started an important and fruitful line of research which has carried the computation of the Kirchhoff index into some symmetrical networks such as distance-regular grahs or circulant graphs. Moreover, a wide range of generalized Kirchhoff indexes for some networks have been introduced. The objective of the present work is to obtain the Kirchhoff index for composite networks such as corona or cluster networks.