Neighborhood Zagreb NM₁(G) = Σ S(v)² where S(v) = Σ d(neighbors). Second-order version of M₁: replaces d(v) with S(v). Mondal-De-Pal (2019). More discriminating: isospectral graphs can have different NM₁. Better for complex molecular prediction.
How to Use
Select graph:
- NM₁: Neighborhood Zagreb
- S(v)²: Per vertex
- vs M₁: Compare
Better Discrimination
Classical M₁ uses d(v): many non-isomorphic graphs share the same degree sequence. NM₁ uses S(v): captures neighborhood structure beyond degree. Better at distinguishing graphs.
Bounds
For regular d-graphs: NM₁ = n·(d·d)² = n·d⁴. Compare M₁ = n·d² (quadratic). NM₁ grows as d⁴ — much more sensitive to degree.
Step-by-Step Instructions
- 1Select graph.
- 2Compute S(v) for each vertex.
- 3Square each S(v).
- 4Sum all S(v)².
- 5Compare with M₁.