An enumeration of labeled graphs

[Abstract] This paper considers figures with vertices and edges as components, and discusses how many figures there are, with the aim of classifying them. These figures are called graphs. Graphs have been classified for many years on the basis of their various attributes. In this context, we encounter the problem of counting the number of graphs with the given properties. In graph theory, this problem has been called the enumeration problem. This paper considers an enumeration of labeled graphs. Riddell (1951) derived a simple, beautiful equation on an enumeration of labeled graphs. This paper shows a broad applicationof this equation