# Theory of Finite and Infinite Graphs

• Dénes König

## Abstract

Let {A, B, C…} be a set of “points.” If certain pairs of these points are connected by one or more “lines”, the resulting configuration is called a graph. Those points of {A, B, C…} which are connected with at least one point are called vertices of the graph. (Vertices which could be called “isolated” are therefore excluded.) The lines involved are called edges of the graph1. An edge which connects A and B, i.e. whose endpoints are A and B, and which goes to A (and B) we shall designate by AB. It is possible that several edges are designated as AB. If A is an endpoint of edge k, we shall also say that A and k are incident to each other. If the set of vertices and the set of edges of a graph are both finite, the graph is called finite, otherwise infinite. An infinite graph has infinitely many edges but possibly only finitely many vertices (e.g., two vertices can be connected by infinitely many edges.)

## Keywords

Bipartite Graph Star Form Regular Graph Hamiltonian Cycle Finite Graph
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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