Reliability of Complete Cubic Networks under the Condition of g-Good-Neighbor

Fault tolerance is the ability such that a multiprocessor system operates properly in the event of the failure of some of its components. Latifi et al. [IEEE Trans. Comput. 43 (2) (1994) 218–222] proposed the notion of R
^g
-connectivity
$(\kappa ^g)$
of a network modeled by graph G such that at least
$\kappa ^g$
vertices in G should be deleted to disconnect the network, and the minimum degree of every connected component is at least g. This paper establishes
$\kappa ^g(CCN\ (n))=(n-g+1)2^g\ (1\leq g\leq n-2)$
for n-dimensional complete cubic network
$CCN\ (\mathrm n)$
. Fault diagnosability is another important metric for evaluating network reliability and availability. In 2012, Peng et al. [Appl. Math. Comput. 218 (21) (2012) 10406–10412] proposed a novel g-good-neighbor (conditional) diagnosability, which tacitly assumes that every fault-free vertex has at least g fault-free neighbors. In view of
$\kappa ^g\ (CCN\ (n))$
, we show that the g-good-neighbor diagnosability of the complete cubic network CCN(n) under the PMC model (
$(1 \leq g\leq n -2)$
) and the MM
^*
model (
$(1\leq g\leq n-2$
and
$n\geq4)$
) is
$(n-g+2)2^g-1$
, respectively.