Mixed fault diameter of Cartesian graph bundles II - Erveš, Rija (Ars mathematica contemporanea, 2015)
The mixed fault diameter ?$D_{(p, q)}(G)$? is the maximum diameter among all subgraphs obtained from graph ?$G$? by deleting ?$p$? vertices and ?$q$? edges. A graph is ?$(p, q)+$?connected if it remains connected after removal of any ?$p$? vertices and any ?$q$? edges. Let ?$F$? be a connected graph with the diameter?$D(F) > 1$?, and ?$B$ be $(p, q)+$?connected graph. Upper bounds for the mixed fault diameter of Cartesian graph bundle ?$G$? with fibre ?$F$? over the base graph ?$B$? are given. We prove that if ?$q > 0$?, then ?$D_{(p + 1, q)}(G) \le D(F) + D_{(p, q)}(B)$?, and if ?$q = 0$? and ?$p > 0$?, then ?$D_{(p + 1, 0)}(G) \le D(F) + \max \{D_{(p, 0)}(B), D_{(p - 1, 1)}(B)\}$?.
Keywords: cartesian graph bundle; fault tolerance; interconnection network; kartezični grafovski sveženj; mešani okvarni premer; mixed fault diameter; okvarna toleranca; omrežja