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On Topological Invariants of the Product of Graphs

Published online by Cambridge University Press:  20 November 2018

M. Behzad  and
S. E. Mahmoodian
M. Behzad
Affiliation:
The National University of Iran
S. E. Mahmoodian
Affiliation:
Western Michigan University
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We consider ordinary graphs, that is, finite, undirected graphs with no loops or multiple lines. The product (also called cartesian product [4]) G1 × G2 of two graphs G1 and G2 with point sets V1 and V2, respectively, has the cartesian product V1 × V2 as its set of points. Two points (u1, u2) and (v1, v2) are adjacent if u1 = v1 and u2 is adjacent with v2 or u2 = v2 and u1 is adjacent with v1.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 2 , April 1969 , pp. 157 - 166
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Behzad, M. and Chartrand, G., An introduction to total graphs. Theory of graphs; International Symposium, Rome 1966. (Gordon and Breach, New York, 1967).Google Scholar
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3. Rosenfeld, M., On the total chromatic number of certain graphs (to appear).Google Scholar
4. Sabidussi, G., Graph multiplication. Math. Z. 72 (1960) 446–457.Google Scholar
5. Vizing, V.G., On an estimate of the chromatic class of a p-graph. Diskret. analiz. 3 (1964) 25–30.Google Scholar