Da Fonseca C.M., Saenpholphat V., Zhang P. Extremal values for a γ-labeling of a cycle with a triangle. Utilitas Mathematica. Vol 92, No. (2013), p.167-185. Retrieved from: https://hdl.handle.net/20.500.14740/6515
For any graph G of order n and size m, a γ-labeling of G is defined as a one-to-one function f: V(G) → {0, 1, ..., m} that induces an edge-labeling f′: E(G) → {1, 2, ..., m} on G defined by f′(uv) = |f(u) - f(v)|, for each edge uv in E(G). The value of f is defined by val(f) = ΣeεE(G) f′ (e). In this paper, we determine the extremal values of a γ-labeling of a cycle with a triangle. Several examples are considered. More generally, for a nonnegative integer δ, we define a γδ-labeling of G as a one-to-one function f : V(G) → {0, 1, ..., m+δ-1, m+δ} that induces an edge-labeling f′: E(G) → {1, 2, ..., m + δ} on G defined by f′(uv) = |f(u) - f(v)|, for each edge uv in E(G). The value of a γδ-labeling f is defined by val(f) = ΣeεE(G) f′ (e). We determine the extremal values of a γδ-labeling of some graphs.
