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Within the last year, two novel ideas optimising the pixel design for a vertex detector have been developed.
For a vertex set X, the set of arcs of D entering (resp. leaving) X is denoted by (resp. ).
For a vertex (v in V(G)), let (N v)) be the set of all neighbors of v in G.
The simplest centrality for a vertex is its node degree, i.e., the total number of edges incident upon a node.
We study the problem of searching for a vertex with a desired property in the arrangement of a set of lines in the plane.
For a vertex i with (k_{i}) neighbors, there is a possibility of (k_{i} k_{i} - )1)/2 edges among the neighbors of vertex i.
To obtain the rank for a vertex based on the list of values for a centrality metric, we first sort the values (in ascending order).
Although these structures allocate |V|−1 space, at most |A d j[v]| of them (one for each neighbor) will be used for a vertex v.
For a vertex subset (V') of G, let (G-V') denote the graph formed from G by deleting all the vertices in (V') and their incident edges.
Following the notation defined in [9] jointly with the one previously introduced in this paper, it is feasible to formally define the set MPR for a vertex as.
For a vertex v in T, let T v denote the subtree induced from T by all descendants of v including v.
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