In this paper the concept of reducibility in graph theory is discussed, and the deletable vertex (edge) in graph (digraph) is defined. The class of graphs (digraphs) ℛ is called vertex (edge) reducible if for any G∈ ℛ either ℛ is the trivial graph (null graph) or it contains a vertex (edge) v such that G-v∈ ℛ. We introduce some classes of graphs (digraphs) which are reducible and others which are not. The vertex reducibility and edge reducibility of Eulerian graphs and Eulerian digraphs have also been studied.
Attar, Akram B.
Reducibility of Eulerian Graphs and Digraphs,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 8,
2, Article 24.
Available at: https://digitalcommons.pvamu.edu/aam/vol8/iss2/24