Further results on radial graphs

Kumarappan Kathiresan; G. Marimuthu

Discussiones Mathematicae Graph Theory (2010)

  • Volume: 30, Issue: 1, page 75-83
  • ISSN: 2083-5892

Abstract

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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.

How to cite

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Kumarappan Kathiresan, and G. Marimuthu. "Further results on radial graphs." Discussiones Mathematicae Graph Theory 30.1 (2010): 75-83. <http://eudml.org/doc/270943>.

@article{KumarappanKathiresan2010,
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.},
author = {Kumarappan Kathiresan, G. Marimuthu},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {radius; diameter; radial graph},
language = {eng},
number = {1},
pages = {75-83},
title = {Further results on radial graphs},
url = {http://eudml.org/doc/270943},
volume = {30},
year = {2010},
}

TY - JOUR
AU - Kumarappan Kathiresan
AU - G. Marimuthu
TI - Further results on radial graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2010
VL - 30
IS - 1
SP - 75
EP - 83
AB - 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.
LA - eng
KW - radius; diameter; radial graph
UR - http://eudml.org/doc/270943
ER -

References

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  1. [1] J. Akiyama, K. Ando and D. Avis, Eccentric graphs, Discrete Math. 16 (1976) 187-195. 
  2. [2] 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. 
  3. [3] R. Aravamuthan and B. Rajendran, On antipodal graphs, Discrete Math. 49 (1984) 193-195, doi: 10.1016/0012-365X(84)90117-1. 
  4. [4] F. Buckley and F. Harary, Distance in Graphs (Addison-Wesley Reading, 1990). Zbl0688.05017
  5. [5] 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 Zbl0959.90062
  6. [6] KM. Kathiresan and G. Marimuthu, A study on radial graphs, Ars Combin. (to appear). Zbl1249.05095
  7. [7] KM. Kathiresan, Subdivision of ladders are graceful, Indian J. Pure Appl. Math. 23 (1992) 21-23. Zbl0739.05076
  8. [8] R.R. Singleton, There is no irregular Moore graph, Amer. Math. Monthly 7 (1968) 42-43, doi: 10.2307/2315106. Zbl0173.26303
  9. [9] D.B. West, Introduction to Graph Theory (Prentice-Hall of India, New Delhi, 2003). 

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