On m-restricted edge connectivity of undirected generalized De Bruijn graphs

This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae, and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand, or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. An m-restricted edge cut is an edge cut of a connected graph whose removal results in components of order at least m, the minimum cardinality over all m-restricted edge cuts of a graph is its m-restricted edge connectivity. It is known that telecommunication networks with topology having larger m-restricted edge connectivity are locally more reliable for all m ≤ 3. This work shows that if n ≥ 7, then undirected generalized binary De Bruijn graph UB G (2, n) is maximally m-restricted edge connected for all m ≤ 3, where a graph G is maximally m-restricted edge connected if its m-restricted edge connectivity is equal to the minimum number of edges from any connected subgraphs S to G − S.