Geodesic
A Canonical Factorization for Graph Homomorphisms
Canadian journal of mathematics, Tome 29 (1977) no. 4, pp. 738-743

Voir la notice de l'article provenant de la source Cambridge University Press

The graphs are undirected, without loops or multiple edges. The edge set E(X) of a graph X is a set of certain unordered pairs [x, y] of distinct elements of the vertex set V(X). For x ε V(X) we denote by E(x; X) the edges of X incident with x. A (homo)morphism φ : X ⟶ Y is a function from V(X) to V(Y) which preserves edges; thus it induces φ # : E(X) ⟶ E(Y) by φ # [x, x’] = [φx, φx’]. 
Fawcett, Barry. A Canonical Factorization for Graph Homomorphisms. Canadian journal of mathematics, Tome 29 (1977) no. 4, pp. 738-743. doi: 10.4153/CJM-1977-077-3
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