Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-28T05:01:58.080Z Has data issue: false hasContentIssue false
  • English
  • Français

A graph and its complement with specified properties V: The self-complement index

Part of: Graph theory

Published online by Cambridge University Press:  26 February 2010

Jin Akiyama ,
Geoffrey Exoo  and
Frank Harary
Jin Akiyama
Affiliation:
University of Michigan, Department of Mathematics, Ann Arbor, M1 48109, U.S.A.
Geoffrey Exoo
Affiliation:
University of Michigan, Department of Mathematics, Ann Arbor, M1 48109, U.S.A.
Frank Harary
Affiliation:
University of Michigan, Department of Mathematics, Ann Arbor, M1 48109, U.S.A.
Get access

Abstract

The self-complement index s(G) of a graph G is the maximum order of an induced subgraph of G whose complement is also induced in G. This new graphical invariant provides a measure of how close a given graph is to being selfcomplementary. We establish the existence of graphs G of order p having s(G) = n for all positive integers n < p. We determine s(G) for several families of graphs and find in particular that when G is a tree, s(G) = 4 unless G is a star for which s(G) = 2.

MSC classification

Secondary: 05C99: None of the above, but in this section
Type
Research Article
Information
Mathematika , Volume 27 , Issue 1 , June 1980 , pp. 64 - 68
Copyright
Copyright © University College London 1980

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Akiyama, J. and Harary, F.. “A graph and its complement with specified properties III: Girth and circumference”, Int'l J. Math, and Math. Sci., 2 (1979), 685–692.CrossRefGoogle Scholar
2.Akiyama, J. and Harary, F.. “A graph and its complement with specified properties IV: Counting selfcomplementary blocks”, J. Graph Theory, to appear.Google Scholar
3.Harary, F.. Graph theory (Addison-Wesley, Reading, Massachusetts, 1969).CrossRefGoogle Scholar
4.Harary, F. and Read, R. C.. “Is the null graph a pointless concept?” Graphs and combinatorics (Bari, R. and Harary, F., eds.), Springer Lecture Notes, 406 (1974), 37–44.CrossRefGoogle Scholar