What is a "non-trivial connected graph"? What is a "non-trivial component"? I am solving some graph theory problems and need clarification on the definitions of these terms.
Can anyone explain the terms with examples?
What is a Non-Trivial Connected Graph?
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graph-theory
terminology
1 Answers
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The trivial graph is the graph on one vertex. This graph meets the definition of connected vacuously (since an edge requires two vertices). A non-trivial connected graph is any connected graph that isn't this graph.
A non-trivial connected component is a connected component that isn't the trivial graph, which is another way of say that it isn't an isolated point.