Further results on radial graphs
Treść / Zawartość
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.
-  J. Akiyama, K. Ando and D. Avis, Eccentric graphs, Discrete Math. 16 (1976) 187-195.
-  R. Aravamuthan and B. Rajendran, Graph equations involving antipodal graphs, Presented at the seminar on Combinatorics and applications held at ISI (Culcutta during 14-17 December 1982) 40-43.
-  R. Aravamuthan and B. Rajendran, On antipodal graphs, Discrete Math. 49 (1984) 193-195, doi: 10.1016/0012-365X(84)90117-1.
-  F. Buckley and F. Harary, Distance in Graphs (Addison-Wesley Reading, 1990).
-  G. Chartrand, W. Gu, M. Schultz and S.J. Winters, Eccentric graphs, Networks 34 (1999) 115-121, doi: 10.1002/(SICI)1097-0037(199909)34:2<115::AID-NET4>3.0.CO;2-K
-  KM. Kathiresan and G. Marimuthu, A study on radial graphs, Ars Combin. (to appear).
-  KM. Kathiresan, Subdivision of ladders are graceful, Indian J. Pure Appl. Math. 23 (1992) 21-23.
-  R.R. Singleton, There is no irregular Moore graph, Amer. Math. Monthly 7 (1968) 42-43, doi: 10.2307/2315106.
-  D.B. West, Introduction to Graph Theory (Prentice-Hall of India, New Delhi, 2003).