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Despite not using any global topological information, they guarantee O(n3) hitting and cover times for any graph, where n is the order of the graph.
It follows from Eq. (1.4), Corollary 3.2, and Theorem 3.1 that the order of the graph (the numbers of vertices in the graph) is the algebraic multiplicity of γ, q k are 1 plus the distance between vertices ( ⌈ n 2 ⌉ + k, 0, ⌈ n 2 ⌉ − k ) and ( ⌈ n 2 ⌉ − k, 0, ⌈ n 2 ⌉ + k ), and the numbers of vertices in the n th height of the graph is the geometric multiplicity of γ.
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Instead, we re-arranged the order of the graphs in Figure 5, to facilitate comparison between the two figures.
The order of the color changes for a given node is determined by the order of the graphs used to generate the animation.
Thus, the schedule period must be greater than or equal to T K =γ min +m+1, where m is the order of the conflict graph.
We can achieve much better running times if the number of involved subgraphs is small compared to the order of the original graph and the shortest path problems restricted to these subgraphs is computationally easy.
The order of the 32 graphs was randomly defined for each expert and each round, except for the duplicate seasons which positions were non-consecutive, selected at random, and fixed for all experts and all rounds, in order to avoid neighbouring duplicates.
The order of a graph is the number of its nodes and the size is the number of interactions.
After N - 1 iterations, where N is the order of the building layout graph, the complete MST is found.
In this section, we always assume that the order of a graph is n = 2 k.
Precedence defines a partial order on the SCCs of the graph G.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com