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The component connectivity is the generalization of connectivity which is an parameter for the reliability evaluation of interconnection networks. The $g$-component connectivity $ckappa_{g}(G)$ of a non-complete connected graph $G$ is the minimum number of vertices whose deletion results in a graph with at least $g$ components. The results in [Component connectivity of the hypercubes, International Journal of Computer Mathematics 89 (2012) 137-145] by Hsu et al. determines the component connectivity of the hypercubes. As an invariant of the hypercube, we determine the $(g+1)$-component connectivity of the folded hypercube $ckappa_{g}(FQ_{n})=g(n+1)-frac{1}{2}g(g+1)+1$ for $1leq g leq n+1, ngeq 8$ in this paper.
As a generalization of vertex connectivity, for connected graphs $G$ and $T$, the $T$-structure connectivity $kappa(G, T)$ (resp. $T$-substructure connectivity $kappa^{s}(G, T)$) of $G$ is the minimum cardinality of a set of subgraphs $F$ of $G$ that
The $g$-component edge connectivity $clambda_g(G)$ of a non-complete graph $G$ is the minimum number of edges whose deletion results in a graph with at least $g$ components. In this paper, we determine the component edge connectivity of the folded hy
The generalized $k$-connectivity of a graph $G$, denoted by $kappa_k(G)$, is a generalization of the traditional connectivity. It is well known that the generalized $k$-connectivity is an important indicator for measuring the fault tolerance and reli
As a generalization of the traditional connectivity, the g-component edge connectivity c{lambda}g(G) of a non-complete graph G is the minimum number of edges to be deleted from the graph G such that the resulting graph has at least g components. Hype
We introduce the notion of a symmetric basis of a vector space equipped with a quadratic form, and provide a sufficient and necessary condition for the existence to such a basis. Symmetric bases are then used to study Cayley graphs of certain extrasp