Question

Eccentricity of a vertex denoted by e(v) is defined by-

• A. max$\left\{d\right(u,v):uϵv,u\ne v\}$ (where d (u,v) is the distance of vertex u and vertex v)
• B. min $\left\{d\right(u,v):uϵv,u\ne v\}$
• C. Both 1 and 2
• D. None of these

Answer 1

The correct option is A max$\left\{d\right(u,v):uϵv,u\ne v\}$ (where d (u,v) is the distance of vertex u and vertex v)

Eccentricity of a vertex denoted by e(v) is defined by max{d(u,v):uϵv,u≠v}{d(u,v):uϵv,u≠v} (where d (u,v) is the distance of vertex u and vertex v).

The maximum distance between a vertex to all other vertices is considered as the eccentricity of vertex. 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.