Distance Compatible Set-Labeling Index 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; G is distance compatible set-labeled (or, ‘dcsl’) graph if it admits a dcsl. A dcsl f of a graph G is k-uniform dcsl if the constants of proportionality k (x,y) , (x, y) ∈ V (G) × V (G) are all equal to k; G itself is a k-uniform dcsl graph if it admits a k-uniform dcsl. We define the dcsl index δd of graph G as the minimum cardinality of the ground set X such that G admits a dcsl. In this paper we calculate the 1-uniform dcsl index of some classes of graphs.
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