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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.

MSC:
05C99 Graph theory
05C38 Paths and cycles
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References:
[1] HARARY F., NORMAN R. Z.: The dissimilarity characteristic of Husimi trees. Ann Math. 58, 1953, 134-141. · Zbl 0051.40502
[2] HARARY F.: Graph Theory. Addison-Wesley, Reading, MA, 1969. · Zbl 0196.27202
[3] MITCHEL HEDETNIEMI S. L., HEDETNIEMI S. T., SLATER P. J.: Centers and medians of C(n)-trees. Utilitas Math. 21C, 1982, 225-235. · Zbl 0504.05054
[4] JORDAN C.: Sur les assemblages des lignes. J. Reine Anew. Math. 70, 1869, 185-190. · JFM 02.0344.01
[5] PROSKUROWSKI A.: Centers of maximal outerplanar graphs. J. Graph Theory. 4, 1980, 75-79. · Zbl 0401.05065
[6] PROSKUROWSKI A.: Centers of 2-trees. Ann. of Discrete Math. 9, 1980, 1-5. · Zbl 0449.05018
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