The integrity of small cage graphs. (English) Zbl 1179.05063
Summary: Integrity, a measure of network reliability, is defined as
\[ I(G)= \min_{S\subset V} \{|S|+m(G-S)\}, \]
where \(G\) is a graph with vertex set \(V\) and \(m(G-S)\) denotes the order of the largest component of \(G-S\). In this article the integrity of the cubic cage graph \((3,g)\) up to \(g=10\) and the integrity of the known small cages with less than or equal to 60 vertices is computed.
\[ I(G)= \min_{S\subset V} \{|S|+m(G-S)\}, \]
where \(G\) is a graph with vertex set \(V\) and \(m(G-S)\) denotes the order of the largest component of \(G-S\). In this article the integrity of the cubic cage graph \((3,g)\) up to \(g=10\) and the integrity of the known small cages with less than or equal to 60 vertices is computed.
MSC:
| 05C40 | Connectivity |
