✦ LIBER ✦

On eccentric vertices in graphs

✍ Scribed by Chartrand, Gary; Schultz, Michelle; Winters, Steven J.

Publisher: John Wiley and Sons
Year: 1996
Tongue: English
Weight: 387 KB
Volume: 28
Category: Article
ISSN: 0028-3045
DOI: 10.1002/(sici)1097-0037(199612)28:4<181::aid-net2>3.0.co;2-h

No coin nor oath required. For personal study only.

✦ Synopsis

The eccentricity e(u) of a vertex u in a connected graph G is the distance between u and a vertex furthest from u. The minimum eccentricity among the vertices of G is the radius rad G of G, and the maximum

The radial number m(u) of u is the minimum eccentricity among the eccentric vertices of u, while the diametrical number dn(u) of u is the maximum eccentricity among the eccentric vertices of u. The radial number m(G) of G is the minimum radial number among the vertices of G and the diametrical number dn(G) of G is the minimum diametrical number among the vertices of G. Several results concerning eccentric vertices are presented. It is shown that for positive integers a and b with a 5 b 5 2a there exists a connected graph G having rn(G) = a and dn(G) = b. Also, if a, b , and c are positive integers with a s b s c s 2a, then there exists a connected graph G with rad G = a, m(G) = b , and diam G = c.

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