Mixed fault diameter of Cartesian graph bundles

Authors:
Rija Erveš;Janez Erovnik
Affiliations:
Institute of Mathematics, Physics and Mechanics, Jadranska 19, Ljubljana 1000, Slovenia and FCE, University of Maribor, Smetanova 17, Maribor 2000, Slovenia;Institute of Mathematics, Physics and Mechanics, Jadranska 19, Ljubljana 1000, Slovenia and FME, University of Ljubljana, Aškerčeva 6, Ljubljana 1000, Slovenia
Venue:
Discrete Applied Mathematics
Year:
2013

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Abstract

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 the removal of any p vertices and any q edges. Let F be a (p,q)+connected graph and BK"2 be a connected graph. Upper bounds for the mixed fault diameter of the Cartesian graph bundle G with fibre F are given. We prove that if q0, then D"("p"+"1","q")(G)@?D"("p","q")(F)+D(B), where D(B) denotes the diameter of B. If q=0 and p0, then D"("p"+"1","0")(G)@?max{D"("p","0")(F),D"("p"-"1","1")(F)}+D(B). In the case when p=q=0, the fault diameter is determined exactly.