Upper Bounds on the Radio Number of Some Trees
نویسندگان
چکیده
Abstract: Let G be a simple,connected and undirected graph with diameter d. For a positive integer k (≤ d), a radio k-labeling f of G is an assignment of non-negative integers, called labels to the vertices of G such that if u, v ∈ V (G) are distinct then d(u, v) + |f(u) − f(v)| ≥ k + 1 where d(u, v) is the distance between u and v. The maximum label (positive integer) assigned by f to some vertex of G is called the span of f . The radio number of G denoted by rn(G) is the minimum span over all radio d-labelings of G. In this paper, we prove an upper bound for the radio number of binomial tree, Fibonacci trees and uniform caterpillar.
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