Geodesic
Some relations between distance-based polynomials of trees
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 30 (2005), p. 1 .

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The Hosoya polynomial $H(G,\lambda)$ of a graph $G$ has the property that its first derivative at $\lambda=1$ is equal to the Wiener index. Sometime ago two distance-based graph invariants were studied -- the Schultz index $S$ and its modification $S^\ast$ . We construct distance--based graph polynomials $H_1(G,\lambda)$ and $H_2(G,\lambda)$ , such that their first derivatives at $\lambda=1$ are, respectively, equal to $S$ and $S^\ast$ . In case of trees, $H_1(G,\lambda)$ and $H_2(G,\lambda)$ are related with $H(G,\lambda)$ .
DOI : 10.2298/BMAT0530001G
Classification : 05C12 05C05
Keywords: Graph polynomial, distance (in graph), tree, Wiener index, Schultz index 
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     title = {Some relations between distance-based polynomials of trees},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
     pages = {1 },
     publisher = {mathdoc},
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     zbl = {1120.05304},
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     url = {http://geodesic.mathdoc.fr/articles/10.2298/BMAT0530001G/}
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I. Gutman. Some relations between distance-based polynomials of trees. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 30 (2005), p. 1 . doi : 10.2298/BMAT0530001G. http://geodesic.mathdoc.fr/articles/10.2298/BMAT0530001G/

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