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# Vulnerability of super connected split graphs and bisplit graphs

• * Corresponding author: Bernard L. S. Lin
• A graph $G = (C, I, E)$ is called a split graph if its vertex set $V$ can be partitioned into a clique $C$ and an independent set $I$. A graph $G = (Y \cup Z, I, E)$ is called a bisplit graph if its vertex set $V$ can be partitioned into three stable sets $I, Y,Z$ such that $Y \cup Z$ induces a complete bipartite graph and an independent set $I$. A connected graph $G$ is called supper-$κ$ (resp. super-$λ$) if every minimum vertex cut (edge cut) of $G$ is the set of neighbors of some vertex (the edges of incident to some vertex) in $G$. In this note, we show that: split graphs and bisplit graphs are super-$κ$ and super-$λ$.

Mathematics Subject Classification: Primary: 05C40; Secondary: 05C90.

 Citation:

• Figure 1.  $G$ is not super-$\kappa$

Figure 2.  $G$ is not super-$\lambda$

Figure 3.  $G$ is not super-$\lambda$

Figure 4.  shuttle graph

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