The Kirchhoff Index of Folded Hypercubes and Some Variant Networks

The Kirchhoff Index of Hypercubes and Related Complex Networks

The resistance distance between any two vertices of G is defined as the network effective resistance between them if each edge of G is replaced by a unit resistor. The Kirchhoff index Kf(G) is the sum of resistance distances between all the pairs of vertices in G. We firstly provided an exact formula for the Kirchhoff index of the hypercubes networks Q n by utilizing spectral graph theory. More...

Cycles in folded hypercubes

This work investigates important properties related to cycles of embedding into the folded hypercube FQn for n ≥ 2. The authors observe that FQn is bipartite if and only if n is odd, and show that the minimum length of odd cycles is n + 1 if n is even. The authors further show that every edge of FQn lies on a cycle of every even length from 4 to 2n; if n is even, every edge of FQn also lies on ...

The Kirchhoff indexes of some composite networks

In electric circuit theory, it is of great interest to compute the effective resistance between any pair of vertices of a network, as well as the Kirchhoff index. During the past decade these parameters have been applied in organic chemistry as natural structural indexes different from the usual ones in order to achieve an improvement in the discrimination between different molecules that have ...

Edge-fault-tolerant properties of hypercubes and folded hypercubes

On conditional diagnosability of the folded hypercubes

The n-dimensional folded hypercube FQn, a variation of the hypercube proposed by Ahmed et al. [A. El-Amawy, S. Latifi, Properties and performance of folded hypercubes, IEEE Transactions on Parallel and Distributed Systems 2(3) (1991) 31–42], is an (n + 1)-regular (n + 1)-connected graph. Conditional diagnosability, a new measure of diagnosability introduced by Lai et al. [Pao-Lien Lai, Jimmy J....