2 research outputs found
The g-extra connectivity of the Mycielskian
The -extra connectivity is an important parameter to measure the ability
of tolerance and reliability of interconnection networks. Given a connected
graph and a non-negative integer , a subset is
called a -extra cut of if is disconnected and every component of
has at least vertices. The cardinality of the minimum -extra cut
is defined as the -extra connectivity of , denoted by . In a
search for triangle-free graphs with arbitrarily large chromatic numbers,
Mycielski developed a graph transformation that transforms a graph into a
new graph , which is called the Mycielskian of . This paper
investigates the relationship of the g-extra connectivity of the Mycielskian
and the graph , moreover, show that
for and
From Graph Isoperimetric Inequality to Network Connectivity -- A New Approach
We present a new, novel approach to obtaining a network's connectivity. More
specifically, we show that there exists a relationship between a network's
graph isoperimetric properties and its conditional connectivity. A network's
connectivity is the minimum number of nodes, whose removal will cause the
network disconnected. It is a basic and important measure for the network's
reliability, hence its overall robustness. Several conditional connectivities
have been proposed in the past for the purpose of accurately reflecting various
realistic network situations, with extra connectivity being one such
conditional connectivity. In this paper, we will use isoperimetric properties
of the hypercube network to obtain its extra connectivity. The result of the
paper for the first time establishes a relationship between the age-old
isoperimetric problem and network connectivity.Comment: 17 pages, 0 figure