We show that planar embeddable 3-connected Laman graphs are generically non-soluble. A Laman graph represents a configuration of points on the Euclidean plane with just enough distance specifications between them to ensure rigidity. Formally, a Laman graph is a maximally independent graph, that is, one that satisfies the vertex-edge count 2v − 3 = e together with a corresponding inequality for ...

We show that planar embeddable 3-connected CAD graphs are generically non-soluble. A CAD graph represents a configuration of points on the Euclidean plane with just enough distance dimensions between them to ensure rigidity. Formally, a CAD graph is a maximally independent graph, that is, one that satisfies the vertex-edge count 2v − 3 = e together with a corresponding inequality for each subgr...

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For a graph G, the P2-path graph, P2(G), has for vertices the set of all paths of length 2 in G. Two vertices are connected when their union is a path or a cycle of length 3. We present lower bounds on the edge-connectivity, (P2(G)) of a connected graph G and give conditions for maximum connectivity. A maximally edge-connected graph is superif each minimum edge cut is trivial, and it is optimum...

in recent years due to improvements of technology within automobile industry, design process of advanced driver assistance systems for collision avoidance and traffic management has been investigated in both academics and industrial levels. detection of traffic signs is an effective method to reach the mentioned aims. in this paper a new intelligent driver assistance system based on traffic sig...

In recent years due to improvements of technology within automobile industry, design process of advanced driver assistance systems for collision avoidance and traffic management has been investigated in both academics and industrial levels. Detection of traffic signs is an effective method to reach the mentioned aims. In this paper a new intelligent driver assistance system based on traffic...

A criterion is given for topological stability of Abelian quantum Hall states, and of Luttinger liquids at the boundaries between such states; this suggests a selection rule on states in the quantum Hall hierarchy theory. The linear response of Luttinger liquids to electromagnetic fields is described: the Hall conductance is quantized, irrespective of whether edge modes propagate in different d...