Geodesic
A New Proof of the Szeged-Wiener Theorem
Kragujevac Journal of Mathematics, Tome 35 (2011) no. 1, p. 165 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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The Wiener index $W(G)$ is the sum of distances between all pairs of vertices of a connected graph $G$. For an edge $e$ of $G$, connecting the vertices $u$ and $v$, the set of vertices lying closer to $u$ than to $v$ is denoted by $N_e(u)$. The Szeged index, $Sz(G)$, is the sum of products $|N_u(e)| \times |N_v(e)|$ over all edges of $G$. A block graph is a graph whose every block is a clique. The Szeged-Wiener theorem states that $Sz(G) = W(G)$ holds if and only if $G$ is a block graph. A new proof of this theorem if offered, by means of which some properties of block graphs could be established.
Classification : 05C12 05C05
Keywords: Szeged index, Wiener index, Block graph 
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     title = {A {New} {Proof} of the {Szeged-Wiener} {Theorem}},
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H. Khodashenas; M. J. Nadjafi-Arani; A. R. Ashrafi; I. Gutman. A New Proof of the Szeged-Wiener Theorem. Kragujevac Journal of Mathematics, Tome 35 (2011) no. 1, p. 165 . http://geodesic.mathdoc.fr/item/KJM_2011_35_1_a13/