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Computing the Szeged index
Janez Žerovnik, 1996, original scientific article

Abstract: We give an explicit algorithm for computing the Szeged index of a graph which runs in ▫$O(mn)$▫ time, where ▫$n$▫ is the number of nodes and ▫$m$▫ is the number of edges.
Keywords: mathematics, chemistry, chemical graph theory, molecular graphs, structural formulae, algorithms, topological index, Szeged index
Published: 05.07.2017; Views: 259; Downloads: 47
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Corroborating a modification of the Wiener index
Ivan Gutman, Janez Žerovnik, 2002, short scientific article

Abstract: In a recent work [Chem. Phys. Lett. 333 (2001) 319-321] Nikolić, Trinajstić, and Randie put forward a novel modification ▫$^m$▫W of the Wiener index. We now show that ▫$^m$▫W possesses the basic properties required by a topological index to be acceptable as a measure of the extent of branching of the carbon-atom skeleton of the respective molecule (and therefore to be a structure-descriptor, potentially applicable in QSPR and QSAR studies). In particular, if ▫$T_n$▫ is any n-vertex tree, different from the n-vertex path ▫$P_n$▫ and the n-vertex star ▫$S_n$▫, then mw(Pn) < mW(Tn) < mW(Sn). We also show how the concept of the modified Wiener index can be extended to weighted molecular graphs.
Keywords: graph theory, distance, molecular graphs, modified Wiener index, weigted modified Wiener index, branching, chemical graph theory
Published: 05.07.2017; Views: 279; Downloads: 35
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