labeled directed graph ˂N, E ,l ˃ with N a set of vertices, E⊆ N × N a set of edges

[rkh]

labeled directed graph ˂N, E ,l ˃ with N a set of vertices, E⊆ N × N a set of edges

Given a labeled directed graph ˂N, E ,l ˃ with N a set of vertices, E⊆ N × N a set of edges, and l : E → L a function assigning labels from a set L to edges. Let source and target be functions on E such that source(s,t) = s and target(s,t) = t. Formally formulate the following properties:

i There are no nodes that are target of more than two edges with identical labels.

ii There is at least one path of length three where all the edges have identical labels.

 

[Deleted member 4993]

Given a labeled directed graph ˂N, E ,l ˃ with N a set of vertices, E⊆ N × N a set of edges, and l : E → L a function assigning labels from a set L to edges. Let source and target be functions on E such that source(s,t) = s and target(s,t) = t. Formally formulate the following properties:

i There are no nodes that are target of more than two edges with identical labels.

ii There is at least one path of length three where all the edges have identical labels.

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