Labeled Bipartite Blocks

Abstract

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.