The Kirchhoff Index of Some Combinatorial Networks

الملخص EN

The Kirchhoff index Kf( G ) is the sum of the effective resistance distances between all pairs of vertices in G .

The hypercube Q n and the folded hypercube F Q n are well known networks due to their perfect properties.

The graph G ∗ , constructed from G , is the line graph of the subdivision graph S ( G ) .

In this paper, explicit formulae expressing the Kirchhoff index of ( Q n ) ∗ and ( F Q n ) ∗ are found by deducing the characteristic polynomial of the Laplacian matrix of G ∗ in terms of that of G .