TY - JOUR

T1 - Extended fault-tolerant bipanconnectivity and panconnectivity of folded hypercubes

AU - Kuo, Che Nan

AU - Lee, Chia Wei

AU - Chang, Nai Wen

AU - Shih, Kuang Husn

PY - 2014

Y1 - 2014

N2 - The folded hypercube ( n FQ for short) is a well-known variation of hypercube structure and can be constructed from a hypercube by adding a link to every pair of vertices with complementary addresses. n FQ for any odd n is known to be bipartite. Let f be a faulty vertex in FQn , for n ≥ 2. In addition, let u and v be any two fault-free vertices in {f}. n FQ - f It has been shown that: 1) {f} n FQ - f contains a fault-free path P[u,v] of every length l with dFQn 2 2n 3 FQn d u v + ≤ l ≤ - and 2 | dFQn, FQn l - d u v where n ≥ 2; 2) {f} n FQ - f contains a fault-free P[u,v] path of every length l with n -1≤ l ≤ 2n - 3, where n ≥ 2 is even. In this paper, we extend the above-mentioned result to obtain two further properties as follows: 1) {f} n FQ - f contains a fault-free path P[u,v] of every length l with dFQn 2n 3 FQn d u v ≤ l ≤ - and 2 | dFQn FQn l - d u v for n ≥ 2 ; 2) {f} n FQ - f contains a fault-free path P[u,v] of every length l with n -1≤ l ≤ 2n - 2 for n ≥ 2 is even.

AB - The folded hypercube ( n FQ for short) is a well-known variation of hypercube structure and can be constructed from a hypercube by adding a link to every pair of vertices with complementary addresses. n FQ for any odd n is known to be bipartite. Let f be a faulty vertex in FQn , for n ≥ 2. In addition, let u and v be any two fault-free vertices in {f}. n FQ - f It has been shown that: 1) {f} n FQ - f contains a fault-free path P[u,v] of every length l with dFQn 2 2n 3 FQn d u v + ≤ l ≤ - and 2 | dFQn, FQn l - d u v where n ≥ 2; 2) {f} n FQ - f contains a fault-free P[u,v] path of every length l with n -1≤ l ≤ 2n - 3, where n ≥ 2 is even. In this paper, we extend the above-mentioned result to obtain two further properties as follows: 1) {f} n FQ - f contains a fault-free path P[u,v] of every length l with dFQn 2n 3 FQn d u v ≤ l ≤ - and 2 | dFQn FQn l - d u v for n ≥ 2 ; 2) {f} n FQ - f contains a fault-free path P[u,v] of every length l with n -1≤ l ≤ 2n - 2 for n ≥ 2 is even.

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U2 - 10.1504/IJMC.2014.063655

DO - 10.1504/IJMC.2014.063655

M3 - Article

AN - SCOPUS:84904716912

SN - 1470-949X

VL - 12

SP - 397

EP - 410

JO - International Journal of Mobile Communications

JF - International Journal of Mobile Communications

IS - 4

ER -