Introduction to graph theory
Kirchhoff index of composite graphs
Discrete Applied Mathematics
The Laplacian polynomial and Kirchhoff index of graphs derived from regular graphs
Discrete Applied Mathematics
Note: Comment on "Kirchhoff index in line, subdivision and total graphs of a regular graph"
Discrete Applied Mathematics
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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.