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The degree sequence problem is the problem of finding some or all graphs with the degree sequence being a given non-increasing sequence of positive integers. (Trailing zeroes may be ignored since they are trivially realized by adding an appropriate number of isolated vertices to the graph.) A sequence which is the degree sequence of some simple ...
The degree sequence is a list of numbers in nonincreasing order indicating the number of edges incident to each vertex in the graph. [2] If a simple graph exists for exactly the given degree sequence, the list of integers is called graphic. The Havel-Hakimi algorithm constructs a special solution if a simple graph for the given degree sequence ...
In graph theory, a discipline within mathematics, the frequency partition of a graph (simple graph) is a partition of its vertices grouped by their degree. For example, the degree sequence of the left-hand graph below is (3, 3, 3, 2, 2, 1) and its frequency partition is 6 = 3 + 2 + 1. This indicates that it has 3 vertices with some degree, 2 ...
The Erdős–Gallai theorem is a result in graph theory, a branch of combinatorial mathematics.It provides one of two known approaches to solving the graph realization problem, i.e. it gives a necessary and sufficient condition for a finite sequence of natural numbers to be the degree sequence of a simple graph.
The directed graph realization problem is the problem of finding a directed graph with the degree sequence a given sequence of positive integer pairs. (Trailing pairs of zeros may be ignored since they are trivially realized by adding an appropriate number of isolated vertices to the directed graph.) A sequence which is the degree sequence of ...
If we can tell the degree of every vertex in the graph, we can tell the degree sequence of the graph. [ 5 ] (Vertex-)Connectivity – By definition, a graph is n {\displaystyle n} -vertex-connected when deleting any vertex creates a n − 1 {\displaystyle n-1} -vertex-connected graph; thus, if every card is a n − 1 {\displaystyle n-1} -vertex ...
The graph realization problem is a decision problem in graph theory. Given a finite sequence (, …,) of natural numbers, the problem asks whether there is a labeled simple graph such that (, …,) is the degree sequence of this graph.
It exactly preserves the degree sequence of a given graph by assigning stubs (half-edges) to nodes based on their degrees and then randomly pairing the stubs to form edges. The preservation of the degree sequence is exact in the sense that all realizations of the model result in graphs with the same predefined degree distribution.