Croatica Chemica Acta, Vol. 73 No. 4, 2000.
Original scientific paper
Reverse Wiener Indices
Alexandru T. Balaban
; Natural Resources Research Institute, University of Minnesota-Duluth, 5013 Miller Trunk Highway, Duluth, MN 55811-1442, USA
Denise Mills
; Natural Resources Research Institute, University of Minnesota-Duluth, 5013 Miller Trunk Highway, Duluth, MN 55811-1442, USA
Ovidiu Ivanciuc
; Department of Organic Chemistry, University »Politehnica« of Bucharest, Oficiul 12 CP 243, 78100 Bucharest, Romania
Subhash C. Basak
; Natural Resources Research Institute, University of Minnesota-Duluth, 5013 Miller Trunk Highway, Duluth, MN 55811-1442, USA
Abstract
By subtracting from the graph diameter all topological distances one obtains a new symmetrical matrix, reverse Wiener RW, with zeroes on the main diagonal, whose sums over rows or columns give rise to new integer-number graph invariants σi whose half-sum is a novel topological index (TI), the reverse Wiener index Λ. Analytical forms for values of σi and Λ of several classes of graphs are presented. Relationships with other TIs are discussed. Unlike distance sums, σi values increase from the periphery towards the center of the graph, and they are equal to the graph vertex degrees when the diameter of the graph is equal to 2. Structural descriptors computed from the reverse Wiener matrix were tested in a large number of quantitative structure-property relationship models, demonstrating the usefulness of the new molecular matrix.
Keywords
molecular graph; molecular matrix; structural descriptor; topological index; reverse Wiener matrix; reverse Wiener index; quantitative structure-property relationships
Hrčak ID:
131968
URI
Publication date:
4.12.2000.
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