Abstract
It seems reasonable that for a connected representing graph of a spy network, the more edges it has, the more jeopardy the spy network is in. So, a spy network which has the minimum number of edges is the comparatively reliable network we want. As a special kind of graph, a critically m-neighbor-scattered graph is important and interesting in applications in communication networks. In this paper, we obtain some upper bounds and a lower bound for the size of a minimum critically m-neighbor-scattered graph with given order p and 4 − p ≤ m ≤ − 1. Moreover, we construct a (1 + ∈ )-approximate graph for the minimum critically m-neighbor-scattered graph of order p for sufficiently small m and sufficiently large p.
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Li, F., Ye, Q. (2007). The Size of a Minimum Critically m-Neighbor-Scattered Graph. In: Dress, A., Xu, Y., Zhu, B. (eds) Combinatorial Optimization and Applications. COCOA 2007. Lecture Notes in Computer Science, vol 4616. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73556-4_12
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DOI: https://doi.org/10.1007/978-3-540-73556-4_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73555-7
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