Editing Glossary of graph theory (section)

==W==
{{glossary}}

{{term|W|{{mvar|W}}}}
{{defn|The letter {{mvar|W}} is used in notation for [[wheel graph]]s and [[windmill graph]]s. The notation is not standardized.}}

{{term|Wagner}}
{{defn|no=1|[[Klaus Wagner]]}}
{{defn|no=2|The [[Wagner graph]], an eight-vertex Möbius ladder.}}
{{defn|no=3|[[Wagner's theorem]] characterizing planar graphs by their forbidden minors.}}
{{defn|no=4|Wagner's theorem characterizing the {{math|''K''<sub>5</sub>}}-minor-free graphs.}}

{{term|walk}}
{{defn|A [[Path (graph theory)#Walk, trail, path|walk]] is a finite or infinite [[sequence]] of [[Edge (graph theory)|edges]] which joins a sequence of [[Vertex (graph theory)|vertices]]. Walks are also sometimes called ''chains''.<ref>{{citation|url=https://www.britannica.com/topic/chain-graph-theory|title=Chain - graph theory|website=britannica.com|access-date=25 March 2018}}</ref> A walk is ''open'' if its first and last vertices are distinct, and ''closed'' if they are repeated.}}

{{term|weakly connected}}
{{defn|A {{gli|directed}} graph is called weakly connected if replacing all of its directed edges with undirected edges produces a connected (undirected) graph.}}

{{term|weight}}
{{defn|A numerical value, assigned as a label to a vertex or edge of a graph. The weight of a subgraph is the sum of the weights of the vertices or edges within that subgraph.}}

{{term|weighted graph}}
{{defn|A {{gli|graph}} whose {{gli|vertex|vertices}} or {{gli|edge}}s have been assigned {{gli|weight}}s.  A vertex-weighted graph has weights on its vertices and an edge-weighted graph has weights on its edges.}}

{{term|well-colored}}
{{defn|A [[Grundy number|well-colored graph]] is a graph all of whose [[greedy coloring]]s use the same number of colors.}}

{{term|well-covered}}
{{defn|A [[well-covered graph]] is a graph all of whose maximal independent sets are the same size.}}

{{term|wheel}}
{{defn|A [[wheel graph]] is a graph formed by adding a [[universal vertex]] to a simple cycle.}}

{{term|width}}
{{defn|no=1|A synonym for {{gli|degeneracy}}.}}
{{defn|no=2|For other graph invariants known as width, see {{gli|bandwidth}}, {{gli|branchwidth}}, {{gli|clique-width}}, {{gli|pathwidth}}, and {{gli|treewidth}}.}}
{{defn|no=3|The width of a tree decomposition or path decomposition is one less than the maximum size of one of its bags, and may be used to define treewidth and pathwidth.}}
{{defn|no=4|The width of a [[directed acyclic graph]] is the maximum cardinality of an antichain.}}

{{term|windmill}}
{{defn|A [[windmill graph]] is the union of a collection of cliques, all of the same order as each other, with one shared vertex belonging to all the cliques and all other vertices and edges distinct.}}

{{glossary end}}