Kirchhoff index in line, subdivision and total graphs of a regular graph

Let G be a connected regular graph and l ( G ) , s ( G ) , t ( G ) the line, subdivision, total graphs of G , respectively. In this paper, we derive formulae and lower bounds of the Kirchhoff index of l ( G ) , s ( G ) and t ( G ) , respectively. In particular, we give special formulae for the Kirchhoff index of l ( G ) , s ( G ) and t ( G ) , where G is a complete graph K n , a regular complete bipartite graph K n , n and a cycle C n .

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