Eccentricity of Vertex:-The maximum distance between a vertex to all other vertices is considered as the eccentricity of vertex denoted by e(V).The distance from a particular vertex to all other vertices in the graph is taken and among those distances, the eccentricity is the highest of distances.
For this graph
e(a)=5 e(b)=4 e(c)=3
e(d)=4 e(e)=5 e(f)=5
e(g)=4 e(h)=3 e(i)=4
e(j)=5 e(k)=4 e(l)=5
e(m)=4 e(n)=5
Radius:-The minimum eccentricity from all the vertices is considered as the radius of the Graph G denoted by r(G). The minimum among all the maximum distances between a vertex to all other vertices is considered as the radius of the Graph G.
Here
r(c)=3 and r(h)=3 which is the minimum eccentricity for c and h.
Center:- If the eccentricity of a graph is equal to its radius, then it is known as the central point of the graph. If
e(V) = r(V),
then ‘V’ is the central point of the Graph ’G’.
Here
e(c)=r(c)=3 and e(h)=r(h)=3
Hence,both c and h are center of tree.
Hence,Option(D)c & h is the correct choice.
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