Abstract. For S ⊆ V(G) the S-center and S-centroid of G are defined as the collection of vertices u ∈ V(G) that minimize es(u) = max {d(u, v): v ∈ S} and ds(u) = ∑u∈S d(u, v), respectively. This generalizes the standard definition of center and centroid from the special case of S = V(G).
Harary and Ostrand defined the cutting number c(u) of vertex u in connected graph G to be the number of pairs of vertices {u, w } in G such that u and w are in.
Oct 22, 2024 · The centroid of a graph is a structure composed of nodes closest from all others. This suggests the presence of center of mass average of all ...
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This procedure generalizes the standard definition of center and centroid from the special case of S = V(G) and defines the k-centrum of G to be the subset ...
Aug 24, 2024 · In this paper, we propose a novel solution for finding the center and centroid of a graph by using a multiple source alternating Dijkstra's ...
Oct 12, 2021 · The centroid set consists of vertices such that τ(u)= min v τ(v). We can prove that both sets have size at most 2, one vertex or two adjacent vertices.
Sep 2, 2016 · Here's a problem at CodeForces that asks to find whether each vertex is a centroid, but after removing and replacing exactly one edge at a time.
Dec 2, 2018 · Given an unoriented tree with weightless edges with N vertices and N-1 edges and a number K find K nodes so that every node from a tree is within S distance of ...
It is shown that the distance center and the centroid of a median graph coincide and that the points of a centroid constitute a convex in a median graph.
Feb 24, 2012 · A vertex is central in G if its greatest distance from any other vertex is as small as possible. Is there any algorithm to find central vertex in any given ...