# Cubic graph

From Graph

This article defines a property that can be evaluated to true/false for any undirected graph, and is invariant under graph isomorphism. Note that the term "undirected graph" as used here does not allow for loops or parallel edges, so there can be at most one edge between two distinct vertices, the edge is completely described by the vertices it joins, and there can be no edge from a vertex to itself.

View other such properties

## Contents

## Definition

An undirected graph is termed a **cubic graph** or **trivalent graph** if it is a 3-regular graph, i.e., every vertex of the graph has degree equal to three.

## Relation with other properties

### Stronger properties

Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
---|---|---|---|---|

bicubic graph | cubic bipartite graph |

### Weaker properties

Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
---|---|---|---|---|

regular graph |