Edge-contributions of some topological indices and arboreality of molecular graphs.
Tomaž Pisanski and Janez Žerovnik
Ars mathematica contemporanea Volume 2, Number 1, pp. 49-58, 2009. ISSN 1855-3966

Abstract

Some graph invariants can be computed by summing certain values, called edge-contributions over all edges of graphs. In this note we use edge-contributions to study relationships among three graph invariants, also known as topological indices in mathematical chemistry: Wiener index, Szeged index and recently introduced revised Szeged index. We also use the quotient between the Wiener index and the revised Szeged index to study arboreality (tree-likeness) of graphs.

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