GutmanIndex on LabeledGraph
The sum over the pairs of vertices of the product of their degrees times their distance.
FindStat's St000466, the modified Schultz index, of a connected graph; a pair with no path adds nothing. The graph with no vertices gives 0.
Called as CombinatorialStat(x, "GutmanIndex"). The head's page has its examples.
Live
Distribution
Over LabeledGraphs at each size, tallied here in your browser; sizes past 6 are not offered.
FindStat St000466
The Gutman (or modified Schultz) index of a connected graph.
| Object | Value |
|---|---|
([],1) | 0 |
([(0,1)],2) | 1 |
([(0,2),(1,2)],3) | 6 |
([(0,1),(0,2),(1,2)],3) | 12 |
([(0,3),(1,2),(2,3)],4) | 19 |
([(0,3),(1,3),(2,3)],4) | 15 |
([(0,2),(0,3),(1,2),(1,3)],4) | 32 |
([(0,3),(1,2),(1,3),(2,3)],4) | 27 |
Data from FindStat, the combinatorial statistic finder; the page at findstat.org/St000466 has the rest.