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A criterion for the planarity of the total graph of a graph*

Published online by Cambridge University Press:  24 October 2008

Mehdi Behzad
Mehdi Behzad
Affiliation:
Wayne State University and Pahlavi University, Shiraz, Iran
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Extract

Two well-known numbers associated with a graph G (finite and undirected with no loops or multiple lines) are the (point) chromatic and the line chromatic number of G (see (2)). With G there is associated a graph L(G), called the line-graph of G, such that the line chromatic number of G is the same as the chromatic number of L(G). This concept was originated by Whitney (9) in 1932. In 1963, Sedlâček (8) characterized graphs with planar line-graphs. In this note we introduce the notions of the total chromatic number and the total graph of a graph, and characterize graphs with planar total graphs.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 63 , Issue 3 , July 1967 , pp. 679 - 681
Copyright
Copyright © Cambridge Philosophical Society 1967

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References

REFERENCES

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