CODEWITHSUNDEEP
nodesgraph-theoryvertex
Mate E.
Mate E.

Reputation: 396

Leaf and self loop

Can a node with a self-loop be a leaf node? Or maybe leaf is defined only for simple graphs (no self-loop, no multiple edges)? I can't find the answer. I found various definitions, but nowhere an answer for this.

Upvotes: 0

Views: 1431

Answers (1)

Jan
Jan

Reputation: 11726

A graph with a loop isn't a tree but a graph with a cycle. Leaves are defined for trees only.

Let's take a more formal approach. A self-loop adds 2 to the degree of a vertex, or 1 to both indegree and outdegree in case of directed graphs. Assuming that a leaf is a vertex with outdegree 0 (and indegree 1, but that's guaranteed by a definition of a tree), a vertex with a self-loop cannot be a leaf.

Upvotes: 3

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