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Domination in functigraphs

Linda Eroh, Ralucca Gera, Cong X. Kang, Craig E. Larson, Eunjeong Yi (2012)

Discussiones Mathematicae Graph Theory

Let G₁ and G₂ be disjoint copies of a graph G, and let f:V(G₁) → V(G₂) be a function. Then a functigraph C(G,f) = (V,E) has the vertex set V = V(G₁) ∪ V(G₂) and the edge set E = E(G₁) ∪ E(G₂) ∪ {uv | u ∈ V(G₁), v ∈ V(G₂),v = f(u)}. A functigraph is a generalization of a permutation graph (also known as a generalized prism) in the sense of Chartrand and Harary. In this paper, we study domination in functigraphs. Let γ(G) denote the domination number of G. It is readily seen that γ(G) ≤ γ(C(G,f))...

Edit distance between unlabeled ordered trees

Anne Micheli, Dominique Rossin (2006)

RAIRO - Theoretical Informatics and Applications

There exists a bijection between one-stack sortable permutations (permutations which avoid the pattern (231)) and rooted plane trees. We define an edit distance between permutations which is consistent with the standard edit distance between trees. This one-to-one correspondence yields a polynomial algorithm for the subpermutation problem for (231) pattern-avoiding permutations. Moreover, we obtain the generating function of the edit distance between ordered unlabeled trees and some special ones. For...

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