Hostname: page-component-76fb5796d-9pm4c Total loading time: 0 Render date: 2024-04-28T09:48:41.173Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimisation of quadratic forms associated with graphs

Published online by Cambridge University Press:  18 May 2009

Derek A. Waller
Derek A. Waller
Affiliation:
Department of Pure Mathematics, University College of Swansea, Swansea SA2 8PP
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.

Quadratic forms associated with graphs were introduced over a century ago by Jordan [4]. We are concerned with the optimisation of such quadratic forms, following Motzkin and Straus [5], and we use the setting of categories and functors to express the nice interplay between the algebra and the graph theory. Applications to interchange graphs are also obtained.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 18 , Issue 1 , January 1977 , pp. 79 - 85
Copyright
Copyright © Glasgow Mathematical Journal Trust 1977

References

REFERENCES

1.Cook, C. R., Two characterisations of interchange graphs of complete m-partite graphs, Discrete Math. 8 (1974), 305–311.CrossRefGoogle Scholar
2.Guy, R. K. and Harary, F., On the Möbius ladders, Canad. Math. Bull. 10 (1967), 493–496.CrossRefGoogle Scholar
3.Harary, F., Graph theory (Addison Wesley, 1969).CrossRefGoogle Scholar
4.Jordan, C., Sur les assemblages de lignes, J. Reine Angew. Math. 70 (1869), 185–190.Google Scholar
5.Motzkin, T. S. and Straus, E. G., Maxima for graphs and a new proof of a theorem of Turán, Canad. J. Math. 17 (1965), 533–540.CrossRefGoogle Scholar
6.Wilson, R. J., On the adjacency matrix of a graph, Combinatorics, I.M.A. (1973), 295–321.Google Scholar