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Adding distinct-vertices clarification which is also echoed in the following statement which refers to a complete graph. |
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[[File:Petersen graph complement.svg|thumb|300px|The [[Petersen graph]] (on the left) and its complement graph (on the right).]]
In [[graph theory]], the '''complement''' or '''inverse''' of a graph ''G'' is a graph ''H'' on the same vertices such that two vertices of ''H'' are adjacent [[if and only if]] they are not adjacent in ''G'', and if they are distinct vertices. That is, to generate the complement of a graph, one fills in all the missing edges required to form a [[complete graph]], and removes all the edges that were previously there. It is not, however, the [[complement (set theory)|set complement]] of the graph; only the edges are complemented.
==Formal construction==
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