# E

## Edge

An edge in a graph is an unordered pair of nodes.
In a directed graph, the edges are ordered
pairs.

## Eulerian graph

One containing an Euler cycle.
For (connected) undirected graphs, this is true iff every vertex
has even degree.
For directed graphs, this is true iff every vertex has equal
indegree and outdegree.
Planar bipartite graphs are dual to planar Eulerian graphs
and vice versa.

## Euler's Formula

A formula relating the number of edges, and nodes of a graph to the number
of regions into which it will divide the plane.
Let *G* be a connected planar graph with *n* nodes and
*e* edges which divides
the plane into *r* regions. Then any one of *n, e,* and
*r* may be determined
from the other two by the relation *n-e+r=2*.

## Eulerian Chain

A chain in a graph whose edges are all of the
edges of the graph.

## Eulerian Cycle

A cycle in a graph whose edges are all of the
edges of the graph.

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An On-line Dictionary of Combinatorics