Editing Glossary of graph theory (section)

==L==
{{glossary}}

{{term|L|''L''}}
{{defn|{{math|''L''(''G'')}} is the [[line graph]] of {{mvar|G}}; see {{gli|line}}.}}

{{term|label}}
{{defn|no=1|Information associated with a vertex or edge of a graph. A labeled graph is a graph whose vertices or edges have labels. The terms ''vertex-labeled'' or ''edge-labeled'' may be used to specify which objects of a graph have labels. [[Graph labeling]] refers to several different problems of assigning labels to graphs subject to certain constraints. See also [[graph coloring]], in which the labels are interpreted as colors.}}
{{defn|no=2|In the context of [[graph enumeration]], the vertices of a graph are said to be labeled if they are all distinguishable from each other. For instance, this can be made to be true by fixing a one-to-one correspondence between the vertices and the integers from 1 to the order of the graph. When vertices are labeled, graphs that are isomorphic to each other (but with different vertex orderings) are counted as separate objects. In contrast, when the vertices are unlabeled, graphs that are isomorphic to each other are not counted separately.}}

{{term|leaf}}
{{defn|no=1|A leaf vertex or pendant vertex (especially in a tree) is a vertex whose degree is&nbsp;{{math|1}}. A leaf edge or pendant edge is the edge connecting a leaf vertex to its single neighbour.}}
{{defn|no=2|A [[leaf power]] of a tree is a graph whose vertices are the leaves of the tree and whose edges connect leaves whose distance in the tree is at most a given threshold.}}

{{term|length}}
{{defn|In an unweighted graph, the length of a cycle, path, or walk is the number of edges it uses. In a weighted graph, it may instead be the sum of the weights of the edges that it uses. Length is used to define the [[shortest path]], [[girth (graph theory)|girth]] (shortest cycle length), and [[longest path]] between two vertices in a graph.}}

{{term|level}}
{{defn|no=1|This is the ''depth'' of a node plus 1, although some<ref name="NIST Level">{{citation|url=https://xlinux.nist.gov/dads/HTML/level.html|title=level | publisher = [[NIST]]}}</ref> define it instead to be synonym of ''depth''. A node's level in a rooted tree is the number of nodes in the path from the root to the node. For instance, the root has level 1 and any one of its adjacent nodes has level 2. }}
{{defn|no=2|A set of all node having the same level or depth.<ref  name="NIST Level"/>}}

{{term|line}}
{{defn|A synonym for an undirected edge. The [[line graph]] {{math|''L''(''G'')}} of a graph {{mvar|G}} is a graph with a vertex for each edge of {{mvar|G}} and an edge for each pair of edges that share an endpoint in {{mvar|G}}.}}

{{term|linkage}}
{{defn|A synonym for {{gli|degeneracy}}.}}

{{term|list}}
{{defn|no=1|An [[adjacency list]] is a computer representation of graphs for use in graph algorithms.}}
{{defn|no=2|[[List coloring]] is a variation of graph coloring in which each vertex has a list of available colors.}}

{{term|local}}
{{defn|A local property of a graph is a property that is determined only by the [[Neighbourhood (graph theory)|neighbourhoods]] of the vertices in the graph. For instance, a graph is locally finite if all of its neighborhoods are finite.}}

{{term|loop}}
{{defn|A [[Loop (graph theory)|loop]] or self-loop is an edge both of whose endpoints are the same vertex. It forms a cycle of length {{math|1}}. These are not allowed in simple graphs.}}

{{glossary end}}