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A Note on the Diameter of a Graph

Published online by Cambridge University Press:  20 November 2018

J. A. Bondy
J. A. Bondy*
Affiliation:
Mathematical Institute, Oxford
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The distance d(x, y) between vertices x, y of a graph G is the length of the shortest path from x to y in G. The diameter δ(G) of G is the maximum distance between any pair of vertices in G. i.e. δ(G) = max max d(x, y). In this note we obtain an upper bound

x ε G y ε G

for δ(G) in terms of the numbers of vertices and edges in G. Using this bound it is then shown that for any complement-connected graph G with N vertices

where is the complement of G.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 11 , Issue 3 , August 1968 , pp. 499 - 501
Copyright
Copyright © Canadian Mathematical Society 1968

References

1. Bosák, J., Rosa, A., and Znam, Ś., On decomposition of complete graphs into factors with given diameters. Proceedings of the Colloquium on Theory of Graphs, held at Tihany, Hungary, September 1966, edited by Erdos, P. and Katona, G.. (Academic Press, New York, 1968).Google Scholar