Improved upper bounds for vertex and edge fault diameters of Cartesian graph bundles
arXiv:1212.4670
Abstract
Mixed fault diameter of a graph , $ \D_{(a,b)}(G)$, is the maximal diameter of after deletion of any vertices and any edges. Special cases are the (vertex) fault diameter $\D^V_{a} = \D_{(a,0)}$ and the edge fault diameter $\D^E_{a} = \D_{(0,a)}$. Let be a Cartesian graph bundle with fibre over the base graph . We show that (1) $\D^V_{a+b+1}(G)\leq \D^V_{a}(F)+\D^V_{b}(B)$ when the graphs and are -connected and -connected, , , and provided that $\D_{(a-1,1)}(F)\leq \D^{V}_{a} (F)$ and $\D_{(b-1,1)}(B)\leq \D^{V}_{b} (B)$ and (2) $\D^E_{a+b+1}(G)\leq \D^E_{a}(F)+\D^E_{b}(B)$ when the graphs and are -edge connected and -edge connected, , , and provided that $\D^E_{a}(F)\geq 2$ and $\D^E_{b}(B)\geq 2$.
arXiv admin note: substantial text overlap with arXiv:1002.2508