Discussiones Mathematicae Graph Theory 30(1) (2010) 75-83

FURTHER RESULTS ON RADIAL GRAPHS

Kumarappan Kathiresan

Center for Research and Post Graduate Studies in Mathematics
Ayya Nadar Janaki Ammal College
Sivakasi - 626 124, Tamil Nadu, India
e-mail: kathir2esan@yahoo.com

G. Marimuthu

Department of Mathematics
The Madura College
Madurai - 625 011, Tamil Nadu, India
e-mail: yellowmuthu@yahoo.com

Abstract

In a graph G, the distance d(u,v) between a pair of vertices u and v is the length of a shortest path joining them. The eccentricity e(u) of a vertex u is the distance to a vertex farthest from u. The minimum eccentricity is called the radius of the graph and the maximum eccentricity is called the diameter of the graph. The radial graph R(G) based on G has the vertex set as in G, two vertices u and v are adjacent in R(G) if the distance between them in G is equal to the radius of G. If G is disconnected, then two vertices are adjacent in R(G) if they belong to different components. The main objective of this paper is to characterize graphs G with specified radius for its radial graph.

Keywords: radius, diameter, radial graph.

2010 Mathematics Subject Classification: 05C12.

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Received 17 April 2008
Revised 22 January 2009
Accepted 22 January 2009