# Generalities on Graphs

Chapter
Part of the Surveys and Tutorials in the Applied Mathematical Sciences book series (STAMS, volume 6)

## Abstract

A graph is an abstract concept describing a set of objects where some pairs of objects are connected by links.As mentioned in Notes in the previous chapter, the notion of graphs was implicitly used by Leonhard Euler (1707–1783). Practically, we represent a graph by a diagram in a plane or space consisting of points (vertices) and lines (edges). Lines are allowed to intersect each other. In some applications, say communication networks and electric circuits, a diagram may be associated in a direct way with the objects considered. A crystal structure also provides us with a visible diagram in space when we represent atoms and chemical bonds by points and lines,Strictly speaking, the line representing a bond is virtual. See the beginning part of Chap. 7. respectively. In many other cases, however, a graph structure is not explicitly visible at first hand.

## Keywords

Span Tree Bipartite Graph Regular Graph Homotopy Class Undirected Edge

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