Graph Theory With Applications
Graph Theory With Applications
Computational complexity and bounds for neighbor-scattering number of graphs
ISPAN '05 Proceedings of the 8th International Symposium on Parallel Architectures,Algorithms and Networks
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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 + Ɛ)-approximate graph for the minimum critically m-neighbor-scattered graph of order p for sufficiently small m and sufficiently large p.