Complementary topological indices. (English) Zbl 1542.92220
Summary: An edge of a graph can be geometrically represented by points \((d_r, d_s)\) and \((d_s, d_r)\) in a 2D coordinate system, where coordinates are, obviously, the degrees of the edge’s end-vertices. Recently, using such a geometrical point of view of a graph edge, a couple of topological invariants were put forward. They have attracted considerable attention among chemical graph theorists. This paper introduces a novel approach for devising “geometrical” topological indices. Finally, special attention is focused on the complementary second Zagreb index as a representative of the introduced approach.
MSC:
| 92E10 | Molecular structure (graph-theoretic methods, methods of differential topology, etc.) |
| 05C92 | Chemical graph theory |
| 05C09 | Graphical indices (Wiener index, Zagreb index, Randić index, etc.) |
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