Discussiones Mathematicae Graph Theory 32(1) (2012)
19-29

doi: 10.7151/dmgt.1582

A.P. Santhakumaran
Department of Mathematics |

**Keywords:** median, vertex-to-edge median, edge-to-vertex median, edge-to-edge median

**2010 Mathematics Subject Classification:** 05C12.

[1] | F. Buckley and F. Harary, Distance in Graphs (Addison-Wesley, Reading MA, 1990). |

[2] | F. Buckley, Z. Miller and P.J. Slater, On graphs containing a given graph as center, J. Graph Theory 5 (1981) 427--434, doi: 10.1002/jgt.3190050413. |

[3] | G. Chartrand and P. Zhang, Introduction to Graph Theory (Tata McGraw-Hill, New Delhi, 2006). |

[4] | L.C. Freeman, Centrality in Social networks; 1. Conceptual clarification, Social Networks 1 (1978/79) 215--239, doi: 10.1016/0378-8733(78)90021-7. |

[5] | C. Jordan, Sur les assemblages des lignas, J. Reine Angew. Math. 70 (1869) 185--190, doi: 10.1515/crll.1869.70.185. |

[6] | A.P. Santhakumaran, Center of a graph with respect to edges, SCIENTIA, Series A: Mathematical Sciences 19 (2010) 13--23. |

[7] | P.J. Slater, Some definitions of central structures, preprint. |

[8] | P.J. Slater, Centrality of paths and vertices in a graph , Theory and Applications of Graphs, ed, Gary Chartrand, (John Wiley, 1981) 529--542.: Cores and Pits |

[9] | B. Zelinka, Medians and Peripherians of trees, Arch. Math., Brno (1968) 87--95. |

Received 4 June 2010

Revised 25 December 2010

Accepted 27 December 2010