Level structure

Level structure

In the mathematical subfield of graph theory a level structure of a graph is a partition of the set of vertices into equivalence classes of vertices with the same distance from a given root vertex.

Definition

Given a connected graph "G"=("V","E") with "V" the set of vertices and "E" the set of edges with

:epsilon:V o mathbb{N}

the eccentricity of a vertex, for a given vertex "v"

The partition:V = igcup_{i=0}^{epsilon(v)} L_i(v)=V

with

:L_0(v):={v}:L_i(v):=mathrm{Adj}(L_{i-1}(x)) setminus igcup_{j=0}^{i-1} L_j(x) qquad mbox{ , } i=1,2,ldots epsilon(v)

is called a level structure of "G" with root "v" and depth ε("v").


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