6 research outputs found
Generalized (edge-)connectivity of join, corona and cluster graphs
The generalized -connectivity of a graph , introduced by Hager in 1985, is a natural generalization of the classical connectivity. As a natural counterpart, Li et al. proposed the concept of generalized -edge-connectivity . In this paper, we obtain exact values or sharp upper and lower bounds of and for join, corona and cluster graphs
The generalized 4-connectivity of burnt pancake graphs
The generalized -connectivity of a graph , denoted by , is
the minimum number of internally edge disjoint -trees for any and . The generalized -connectivity is a natural extension of
the classical connectivity and plays a key role in applications related to the
modern interconnection networks. An -dimensional burnt pancake graph
is a Cayley graph which posses many desirable properties. In this paper, we try
to evaluate the reliability of by investigating its generalized
4-connectivity. By introducing the notation of inclusive tree and by studying
structural properties of , we show that for , that is, for any four vertices in , there exist () internally
edge disjoint trees connecting them in