(k, r)-Arithmetic Distance Compatible Set-Labeling of Graphs
نویسندگان
چکیده
Distance compatible set-labeling of a graph G is an injective setassignment f : V (G) → 2X , X a nonempty ground set, such that the corresponding induced function f⊕ : V (G)× V (G) → 2X −{∅}, defined by f⊕(u, v) = f(u) ⊕ f(v) satisfies | f⊕(u, v) |= k (u,v) d(u, v) for all distinct u, v ∈ V (G), where d(u, v) is the distance between u and v, and k (u,v) is a constant, not necessarily an integer. A dcsl f of a (p, q)-graph G is dispersive if the constants of proportionality k uv with respect to f , u = v, u, v ∈ V (G) are all distinct G is (k, r)-arithmetic, if the constants of proportionality with respect to f can be arranged in the arithmetic progression, k, k + r, k +2r, . . . , k + (q − 1)r and if G admits such a dcsl then G is a (k, r)-arithmetic dcslgraph. This paper present our investigations on these new notions.
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