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But it uses grid graphs G that have "holes," that is, G∞−G is not connected.
All grid graphs are bipartite, with the edges connecting an even vertex to an odd vertex.
In order to investigate the algorithm's behavior on large and structured networks, it is analyzed on grid graphs.
In the paper, the authors indicate that it is not known whether or not the Hamilton path problem is NP-complete for grid graphs without holes.
The proposed delay-driven Steiner tree construction method is of O(n2logn) complexity, where n is the number of terminal points and it provides n-approximation solution of the critical time minimization problem for a certain class of grid graphs.
Although the power domination problem has been proved to be NP-complete even when restricted to some special classes of graphs, Dorfling and Henning in [M. Dorfling, M.A. Henning, A note on power domination in grid graphs, Discrete Applied Mathematics 154 (2006) 1023 1027] showed that it is easy to determine the power domination number of an n×m grid.
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A grid graph is a finite vertex-induced subgraph of G∞.
Fig. 11 a The power grid graph of Shandong province of China.
Thus, a grid graph is completely specified by its set of vertices.
Let s and t be distinct vertices of a grid graph G.
For each pair of adjacent nodes in the grid graph, we compute the transition probabilities offline using Eq. (4).
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