Let G = (V, E) be a graph, a vertex labeling f : V → Z2 induces an edge labeling f* : E → Z2 defined by f* (xy) = f (x) + f (y) for each xy ∈ E. For each i ∈ Z2, define vf (i) = | f- 1 (i) | and ef (i) = | f*- 1 (i) |. We call f friendly if | vf (1) - vf (0) | ≤ 1. The full friendly index set of G is the set of all possible values of ef (1) - ef (0), where f is friendly. In this note, we study the full friendly index set of the grid graph P2 × Pn.
Scopus Subject Areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Friendly index