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Kirchhoff index in line, subdivision and total graphs of a regular graph. (English) Zbl 1239.05053
Summary: 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 $C_{n}$.

05C12Distance in graphs
05C62Graph representations
Full Text: DOI
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