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The type of a vertex v of a graph G is the ordered degree sequence of the vertices adjacent to v. The graph G is called vertex-oblique if it contains no two vertices of the same type. We will show that almost every graph G∈G(n,p) is vertex-oblique, if the probability p for each edge to appear in G is within certain bounds.
Let x be a vertex of a simple graph G. The vertex-type of x is the lexicographically ordered degree sequence of its neighbors. We call the graph G vertex-oblique if there are no two vertices in V(G) which are of the same vertex-type. We will show that the set of vertex-oblique graphs of arbitrary connectivity is infinite.
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