# What is minimal edge cover?

## What is minimal edge cover?

A minimal edge cover is an edge cover of a graph that is not a proper subset of any other edge cover. Every minimum edge cover is a minimal edge cover, but the converse does not necessarily hold.

What is edge in edge coverage?

An edge cover of a graph G is a set of edges E c E_c Ec where every vertex in G is incident (touching) with at least one of the edges in E c E_c Ec. This means that each node in the graph is touching at least one of the edges in the edge covering.

### Why is edge coverage better than node coverage?

▶ Node coverage corresponds to statement coverage, edge coverage corresponds to something like branch coverage. Covering all execution paths is impossible with loops, so there are various approximations. Don’t forget the distinction between syntactic and semantic reachability.

What is edge coverage in testing?

Edge coverage reports which branches or code decision points were executed to complete the test. They both report a coverage metric, measured as a percentage. The meaning of this depends on what form(s) of coverage have been used, as 67% branch coverage is more comprehensive than 67% statement coverage.

#### How do you find the minimum vertex cover on a graph?

The size of the minimum vertex cover is 1 (by taking either of the endpoints). 3. Star: |V | − 1 vertices, each of degree 1, connected to a central node. The size of the minimum vertex cover is k − 1 (by taking any less vertices we would miss an edge between the remaining vertices).

What is a minimum edge covering?

A minimum edge covering is an edge covering using the smallest possible number of edges. In the graphs below, the minimum edge covering is indicated by red edges. The edge covering number is is the size of the smallest edge cover of

## What is an edge cover problem?

It is an optimization problem that belongs to the class of covering problems and can be solved in polynomial time . Formally, an edge cover of a graph G is a set of edges C such that each vertex in G is incident with at least one edge in C.

What are the advantages of edge covering?

An edge cover might be a good way to solve a problem if the answer needs to include all nodes of a graph. Many times, themes from edge covering are adapted and integrated into other problems.

### What is the difference between edge cover and maximum matching?

Edge Cover: an edge cover of a graph is a set of edges such that every vertex of the graph is incident to at least one edge of the set [from Wikipedia]. Maximum matching: a matching or independent edge set in a graph is a set of edges without common vertices [from Wikipedia].