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Trees and Tree-Equivalent Graphs

Published online by Cambridge University Press:  20 November 2018

C. Ramanujacharyulu
C. Ramanujacharyulu*
Affiliation:
Indian Statistical Institute, Calcutta
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As is well known in the theory of graphs a tree is a connected graph without cycles. Many characterizing properties of trees are known (1), for example the cyclomatic number is equal to zero, which is also equal to p — 1, where p is the number of connected components of the graph. The graphs with cyclomatic number equal to p — 1 are defined here as tree-equivalent graphs. A tree is always a tree-equivalent graph but not conversely. The properties of tree-equivalent graphs are studied here.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 731 - 733
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Berge, C., Theory of graphs and its applications (London, 19—).Google Scholar
2. Ryser, H. J., Combinatorial properties of matrices of zeros and ones, Can. J. Math., 9 (1957), 371–377.Google Scholar