TITLE:
The Reliability and Fault Tolerance of Conditional Recursive Networks
AUTHORS:
Yilin Song, Yinkui Li
KEYWORDS:
The Generalized -Connectivity, The Generalized -Edge-Connectivity, Conditional Recursive Networks
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.5,
May
8,
2025
ABSTRACT: The generalized
k
-connectivity
κ
k
(
G
)
and
k
-edge-connectivity
λ
k
(
G
)
of a graph
G
are a natural generalization of traditional connectivity
κ(
G
)
and edge connectivity
λ(
G
)
, respectively, which for
κ(
G
)=
κ
2
(
G
)
and
λ(
G
)=
λ
2
(
G
)
. They are important parameters which can often be used to measure the reliability and fault tolerance of interconnection networks. CRNs is a new family of composite networks based on the complete graph, which contain common networks and have the same structural properties as alternating group network, and may also include some unknown networks. In this paper, we investigate the generalized 3-connectivity and 3-edge-connectivity of CRNs, and show that
κ
3
(
G
l,m
)=
λ
3
(
G
l,m
)=m−2
.