On Bounds of Radio Number of Certain Product Graphs
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Date
2018
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Journal of the Nigerian Mathematical Society
Abstract
Given a graph G, whose vertex set is V (G), the radio labelling of G is a variation of vertex labelling of G which satisfy the condition that given any v1, v2 ∈ V (G), and some positive integer function f(v) on V (G), then |f(v1) − f(v2)| ≥ diam(G) + 1 − d(v1, v2). Radio labelling guarantees a better reduction in interference in signal-dependent networks since no two vertex have the same label. The radio number rn(G) of G is the smallest possible value of f(v) such that for any other vk ∈ V (G), f(vk) < f(v). In this work, we consider a Cartesian product graph obtained from a star and a path and determined upper and lower bounds of the radio number for the family of these graphs.
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Citation
Adefokun, T. C. and Ajayi, D. O. (2018). On Bounds of Radio Number of Certain Product Graphs. Journal of the Nigerian Mathematical Society. 37(2); 71-76.