Editing Glossary of graph theory (section)

==I==
{{glossary}}

{{term|in-degree}}
{{defn|The number of incoming edges in a directed graph; see {{gli|degree}}.}}

{{term|incidence}}
{{defn|An [[Incidence (graph)|incidence]] in a graph is a vertex-edge pair such that the vertex is an endpoint of the edge.}}

{{term|incidence matrix}}
{{defn|The [[incidence matrix]] of a graph is a matrix whose rows are indexed by vertices of the graph, and whose columns are indexed by edges, with a one in the cell for row {{mvar|i}} and column {{mvar|j}} when vertex {{mvar|i}} and edge {{mvar|j}} are incident, and a zero otherwise.}}

{{term|incident}}
{{defn|The relation between an edge and one of its endpoints.<ref name="clrs"/>}}

{{term|incomparability}}
{{defn|An incomparability graph is the complement of a [[comparability graph]]; see {{gli|comparability}}.}}

{{term|independent}}
{{defn|no=1|An [[Independent set (graph theory)|independent set]] is a set of vertices that induces an edgeless subgraph. It may also be called a stable set or a coclique. The [[independence number]] {{math|''&alpha;''(''G'')}} is the size of the [[maximum independent set]].}}
{{defn|no=2|In the [[graphic matroid]] of a graph, a subset of edges is independent if the corresponding subgraph is a tree or forest. In the [[bicircular matroid]], a subset of edges is independent if the corresponding subgraph is a [[pseudoforest]].}}

{{term|indifference}}
{{defn|An [[indifference graph]] is another name for a proper interval graph or unit interval graph; see {{gli|proper}}.}}

{{term|induced}}
{{defn|An [[induced subgraph]] or full subgraph of a graph is a subgraph formed from a subset of vertices and from all of the edges that have both endpoints in the subset. Special cases include [[induced path]]s and [[induced cycle]]s, induced subgraphs that are paths or cycles.}}

{{term|inductive}}
{{defn|Synonym for {{gli|degenerate}}.}}

{{term|infinite}}
{{defn|An infinite graph is one that is not finite; see {{gli|finite}}.}}

{{term|internal}}
{{defn|A vertex of a path or tree is internal if it is not a leaf; that is, if its degree is greater than one. Two paths are internally disjoint (some people call it ''independent'') if they do not have any vertex in common, except the first and last ones.}}

{{term|intersection}}
{{defn|no=1|The intersection of two graphs is their largest common subgraph, the graph formed by the vertices and edges that belong to both graphs.}}
{{defn|no=2|An [[intersection graph]] is a graph whose vertices correspond to sets or geometric objects, with an edge between two vertices exactly when the corresponding two sets or objects have a nonempty intersection. Several classes of graphs may be defined as the intersection graphs of certain types of objects, for instance [[chordal graph]]s (intersection graphs of subtrees of a tree), [[circle graph]]s (intersection graphs of chords of a circle), [[interval graph]]s (intersection graphs of intervals of a line), [[line graph]]s (intersection graphs of the edges of a graph), and [[clique graph]]s (intersection graphs of the maximal cliques of a graph). Every graph is an intersection graph for some family of sets, and this family is called an intersection representation of the graph. The [[intersection number (graph theory)|intersection number]] of a graph {{mvar|G}} is the minimum total number of elements in any intersection representation of {{mvar|G}}.}}

{{term|interval}}
{{defn|no=1|An [[interval graph]] is an [[intersection graph]] of [[Interval (mathematics)|intervals of a line]].}}
{{defn|no=2|The interval {{math|[''u'', ''v'']}} in a graph is the union of all shortest paths from {{mvar|u}} to {{mvar|v}}.}}
{{defn|no=3|Interval thickness is a synonym for {{gli|pathwidth}}.}}

{{term|invariant}}
{{defn|A synonym of {{gli|property}}.}}

{{term|inverted arrow}}
{{defn|An {{gli|arrow}} with an opposite {{gli|direction}} compared to another arrow. The arrow {{math|(''y'', ''x'')}} is the inverted arrow of the arrow {{math|(''x'', ''y'')}}.}}

{{term|isolated}}
{{defn|An isolated vertex of a graph is a vertex whose degree is zero, that is, a vertex with no incident edges.<ref name="clrs"/>}}

{{term|isomorphic}}
{{defn|Two graphs are isomorphic if there is an isomorphism between them; see {{gli|isomorphism}}.}}

{{term|isomorphism}}
{{defn|A [[graph isomorphism]] is a one-to-one incidence preserving correspondence of the vertices and edges of one graph to the vertices and edges of another graph. Two graphs related in this way are said to be isomorphic.}}

{{term|isoperimetric}}
{{defn|See {{gli|expansion}}.}}

{{term|isthmus}}
{{defn|Synonym for {{gli|bridge}}, in the sense of an edge whose removal disconnects the graph.}}

{{glossary end}}