Hostname: page-component-7bb8b95d7b-s9k8s Total loading time: 0 Render date: 2024-09-21T11:59:38.581Z Has data issue: false hasContentIssue false
  • English
  • Français

On the line Graph of a Finite Affine Plane

Published online by Cambridge University Press:  20 November 2018

A. J. Hoffman  and
D. K. Ray-Chaudhuri
A. J. Hoffman
Affiliation:
IBM Thomas J. Watson Research Center, Yorktown Heights, New York
D. K. Ray-Chaudhuri
Affiliation:
IBM Thomas J. Watson Research Center, Yorktown Heights, New York
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.

Let n be a finite affine plane with n points on a line. We denote by G(II) the graph whose vertices are all points and lines of II, with two vertices adjacent if and only if one is a point, the other is a line, and the point and line are incident. Let L(11) denote the line graph of G(II), i.e., the vertices of L(II) are the edges of G(II), and two vertices of L(II) are adjacent if the corresponding edges of G(II) are adjacent. It is clear that L(II) is a regular, connected graph with n2(n + 1) vertices and valence 2n — 1.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 687 - 694
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Bose, R. C., Strongly regular graphs, partial geometries and partially balanced designs, Pacific J. Math., 13 (1963), 389–419.Google Scholar
2. Bruck, R. H., Finite nets II, uniqueness and embedding, Pacific J. Math., 13 (1963), 421–457.Google Scholar
3. Hoffman, A. J., On the polynomial of a graph, Amer. Math. Monthly, 70 (1963), 30–36.Google Scholar
4. Hoffman, A. J., On the line graph of a projective plane, to appear in Proc. Amer. Math. Soc.Google Scholar