On the sum of all distances in composite graphs (Q1343276)

The sum of all distances is determined for the results of the following binary operations on graphs: (a) the product \(G_ 1\times G_ 2\), (b) the join \(G_ 1+ G_ 2\), (c) the composition \(G_ 1[G_ 2]\), (d) the corona \(G_ 1\circ G_ 2\) (all these are defined in F. Harary's book of 1969), and (e) the cluster \(G_ 1\{G_ 2\}\) which is obtained by taking one copy of \(G_ 1\) and \(| V(G_ 1)|\) copies of a rooted graph \(G_ 2\) and by identifying the root of the \(i\)th copy of \(G_ 2\) with the \(i\)th vertex of \(G_ 1\) for each \(i\).