The Kirchhoff Index of Folded Hypercubes and Some Variant Networks

Abstract EN

The n-dimensional folded hypercube FQn is an important and attractive variant of the n-dimensional hypercube Qn, which is obtained from Qn by adding an edge between any pair of vertices complementary edges.

FQn is superior to Qn in many measurements, such as the diameter of FQnwhich is ⌈n/2⌉, about a half of the diameter in terms of Qn.

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

In this paper, we established the relationships between the folded hypercubes networks FQn and its three variant networks l(FQn), s(FQn), and t(FQn) on their Kirchhoff index, by deducing the characteristic polynomial of the Laplacian matrix in spectral graph theory.

Moreover, the explicit formulae for the Kirchhoff indexes of FQn, l(FQn), s(FQn), and t(FQn) were proposed, respectively.