Centers and centroids of unicyclic graphs. (English) Zbl 0585.05030

The eccentricity of a vertex u in G is the distance between u and a vertex in G, farthest from u. The subgraph of G induced by the set of vertices with minimum eccentricity is called the center of G. The distance of a vertex u in G is the sum of distances between u and all vertices of G. The subgraph of G induced by the vertices with minimum distance is called the centroid of G. Centers and centroids have been characterized for several classes of graphs like trees, 2-trees and outerplanar graphs. Here we characterize centers and centrois of unicyclic graphs.


05C99 Graph theory
05C38 Paths and cycles
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