Question

A vertex with minimum eccentricity in the graph is called

Answer 1

Answer:

The minimum graph eccentricity is called the graph radius.

Answer 2

Answer:

A vertex with minimum eccentricity in the graph is called radius rad G of G.

Explanation:

• In a linked graph G, the eccentricity e(v) of a vertex v is the distance between v and the vertex furthest from v.
• The radius rad G of G has the lowest eccentricity among its vertices, whereas its diameter diam G has the highest eccentricity.
• If d(u, v) = e, a vertex u of G is termed an eccentric vertex of v. (v).
• The radial number m(v) of v represents the eccentricity vertices' minimum eccentricity, whereas the diametrical number dn(v) represents the eccentricity vertices' maximum the eccentricity.
• G's radial number m(G) is the smallest radial number among its vertices, while G's diametrical number dn(G) is the smallest diametrical number among its vertices.
• A number of findings involving eccentric vertices are given. It is demonstrated that given positive integers a and b with a b 2a, a connected graph G exists with m(G) = a and dn(G) = b.
• Furthermore, if a, b, and c are positive integers with a b c 2a, then a connected graph G exists with rad G = a, m(G) = b, and diam G = c.

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