Abstract
It is known that networks with greater m-restricted edge connectivity are locally more reliable for all m≤4. This work studies the optimization of m-restricted edge connectivity of graphs in the case when m=4. Let G be a connected graph of order at least 8 and Ore(G)= min{d(u)+d(v): u and v are two non-adjacent vertices of graph G }. It is proved in this work that graph G is maximally 4-restricted edge connected if Ore(G) ( |G|+5. This lower bound can be decreased to |G|-1 when G is triangle-free. A class of graphs is presented to exemplify the sharpness of the lower bound.
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Ou, J., Wu, J. (2011). On Optimizing m-Restricted Edge Connectivity of Graphs. In: Wu, Y. (eds) High Performance Networking, Computing, and Communication Systems. ICHCC 2011. Communications in Computer and Information Science, vol 163. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25002-6_7
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DOI: https://doi.org/10.1007/978-3-642-25002-6_7
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