Reformulated first Zagreb EM₁(G) = Σ d(e)² over edges, where d(e) = deg(i)+deg(j)-2 is the edge degree (number of edges adjacent to e). Milićević et al. (2004). Edge-centric Zagreb: applies M₁ idea to the line graph.
How to Use
Select graph:
- EM₁: Reformulated Z.
- d(e): Edge degree
- Line: Graph view
Edge Degree
d(e) for edge e=(i,j) = d(i) + d(j) - 2. It counts edges adjacent to e (not including e itself). In the line graph L(G), d(e) becomes the vertex degree. So EM₁(G) = M₁(L(G))!
Relations
EM₁ relates to vertex indices: EM₁ = F - 2M₂ + M₁ for simple graphs, where F = forgotten index. Elegant connection between edge and vertex perspectives.
Step-by-Step Instructions
- 1Select graph.
- 2Compute edge degrees.
- 3Square each d(e).
- 4Sum all terms.
- 5Verify via M₁,M₂,F.