Graph isomorphism

Builds on Graph

Definition

Let $G$ and $H$ be graphs with vertex sets $V(G)$ and $V(H)$ . A graph isomorphism from $G$ to $H$ is a bijection $f : V(G) \to V(H)$ such that, for all $u, v \in V(G)$ , $u \sim v \text{ in } G \iff f(u) \sim f(v) \text{ in } H.$ The graphs $G$ and $H$ are isomorphic, written $G \cong H$ , if there is an isomorphism between them.

Remarks

Isomorphic graphs have the same number of vertices and edges and the same degrees. They differ only in the names of their vertices. An isomorphism from $G$ to itself is an automorphism of $G$ . The path $P_4$ is isomorphic to its own complement.

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Graph definition
Graph isomorphism definition

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Tag	`00CT0PTH74`
URI	`m2://00CT0PTH74`
Kind	definition
Writing	W1 stated
MSC	05C60
Defines	Graph isomorphism
Uses	Graph

Graph isomorphism

Definition

Remarks

Reading path

Where this leads

Further reading

What this page needs for W2

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