| Abstract
| - The Wiener index W(G) has originally beendefined for acyclic graphs. Therefore its extension tocycle-containing structures is not unambiguous; there are severalpossibilities, some of which have already beenrealized. In this paper, we proposed an “all-path” version ofW and showed that its maximal value is equalto N2(N −1)2N-4, whereN denotes the number of vertices in a graph. Incontrast, the maximal values ofW and its close analogues, the detour index,w(G), and the Szeged index,Sz(G), are polynomials of order4 or less in terms of N, and therefore, it may be expectedthat the new version will discriminate cycle-containing structures more efficiently than W(G),w(G), orSz(G).
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