Hostname: page-component-848d4c4894-nmvwc Total loading time: 0 Render date: 2024-06-25T01:52:24.612Z Has data issue: false hasContentIssue false
  • English
  • Français

A Characterization of Certain Ptolemaic Graphs

Published online by Cambridge University Press:  20 November 2018

David C. Kay  and
Gary Chartrand
David C. Kay
Affiliation:
Michigan State University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

With every connected graph G there is associated a metric space M(G) whose points are the vertices of the graph with the distance between two vertices a and b defined as zero if a = b or as the length of any shortest arc joining a and b if a ≠ b. A metric space M is called a graph metric space if there exists a graph G such that M = M (G), i.e., if there exists a graph G whose vertex set can be put in one-to-one correspondence with the points of M in such a way that the distance between every two points of M is equal to the distance between the corresponding vertices of G.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 342 - 346
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Blumenthal, L., Distance geometry (Oxford, 1953).Google Scholar
2. Harary, Frank, A characterization of block-graphs, Can. Math. Bull., 6 (1963), 1–6.Google Scholar
3. Harary, Frank and Norman, Robert Z., The dissimilarity characteristic of Husimi trees, Ann. Math. (2), 58 (1953), 134–41.Google Scholar
4. Nordhaus, E. A. and Stewart, B. M., Triangles in an ordinary graph, Can. J. Math., 15 (1963), 33–41.Google Scholar
5. Ore, O., Theory of graphs (Providence, 1962).Google Scholar