Cordial Sets of Hypercubes
نویسندگان
چکیده
For a graph G = (V,E) with a binary vertex coloring f : V (G)→ Z2, let vf (i) = |f−1(i)|. We say f is friendly if |vf (1) − vf (0)| ≤ 1, i.e., the number of vertices labeled 1 is the same or almost the same as the number of vertices labeled 0. The coloring f induces an edge labeling f ∗ : E(G) → Z2 defined by f ∗(uv) = f(u) + f(v) (mod 2), for each uv ∈ E(G). Let ef (i) = |{uv ∈ E(G) : f ∗(uv) = i}|. The cordial index of f is the number c(f) = |ef (0) − ef (1)|, and the cordial set of G is C(G) = {c(f) : f is a friendly labeling of G}. In this talk, we discuss the cordial sets of hypercubes.
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