Geodesic
The all-paths transit function of a graph
Czechoslovak Mathematical Journal, Tome 51 (2001) no. 2, pp. 439-448 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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A transit function $R$ on a set $V$ is a function $R\:V\times V\rightarrow 2^{V}$ satisfying the axioms $u\in R(u,v)$, $R(u,v)=R(v,u)$ and $R(u,u)=\lbrace u\rbrace $, for all $u,v \in V$. The all-paths transit function of a connected graph is characterized by transit axioms.
A transit function $R$ on a set $V$ is a function $R\:V\times V\rightarrow 2^{V}$ satisfying the axioms $u\in R(u,v)$, $R(u,v)=R(v,u)$ and $R(u,u)=\lbrace u\rbrace $, for all $u,v \in V$. The all-paths transit function of a connected graph is characterized by transit axioms.
Classification : 05C12, 05C75, 05C99
Keywords: all-paths convexity; transit function; block graph 
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Changat, Manoj; Klavžar, Sandi; Mulder, Henry Martyn. The all-paths transit function of a graph. Czechoslovak Mathematical Journal, Tome 51 (2001) no. 2, pp. 439-448. http://geodesic.mathdoc.fr/item/CMJ_2001_51_2_a16/

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