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Labeled Bipartite Blocks

Published online by Cambridge University Press:  20 November 2018

F. Harary  and
R. W. Robinson
F. Harary
Affiliation:
University of Michigan, Ann Arbor, Michigan
R. W. Robinson
Affiliation:
University of Michigan, Ann Arbor, Michigan
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Graphs which are 2-connected have been called blocks in the graph theoretic literature [3] and stars in the parlance of statistical mechanics [1]. They are also called nonseparable graphs, and in this paper include the complete graph K2 on p = 2 points. The standard terminology of graphical enumeration can be found in [3].

When its points are colored using two distinct colors in such a way that adjacent points receive different colors, a graph is called 2-colored. If the colors are considered interchangeable, such a graph is called bicolored. A graph which can be bicolored is called bicolorable. It is obvious that a connected bicolorable graph has a unique bicoloring, and so one can speak of the sizes of its color classes.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 1 , 01 February 1979 , pp. 60 - 68
Copyright
Copyright © Canadian Mathematical Society 1979

References

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