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Theorem 3.2 Let G be a connected simple graph on n vertices, G σ ∈ D ( G ).
Corollary 3.1 Let G be a connected simple graph of order n, G σ ∈ D ( G ), V ′ ⊂ V ( G ), E ′ ⊂ E ( G ).
Let G be a connected simple graph and let SG be the spectrum of integers v for which there exists a G-design of order v. Put e="{x,y}, with x∈V(G) and y∉V(G).
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A so-called unicyclic graph is a connected simple graph in which the number of edges equals the number of vertices.
Correspondingly, we define a maximally-connected bit-pattern (also referred to as a bit-pattern in this article) to be a connected pattern p where every neighbor bit not in p is 0. We apply a simple region growth algorithm to identify all the maximally-connected patterns in each contact map within the two series of contact maps, corresponding to the two folding trajectories of BBA5.
Based on graph theory, a valid topology in the design domain is represented by a connected simple graph and each edge of the graph is defined by a cubic Bézier curve with varying thickness.
A valid topology in the design domain is ensured by representing the topology as a connected simple graph of nodes.
Let Ω be a simple connected domain, and let C be a simple closed positively oriented contour that lies in Ω.
LetGbe a connected simple Lie group with finite centre, and letΓbe a lattice inG.
Let G be a simple connected graph with n vertices.
Let be a simple connected graph with vertices.
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