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- Title
A Novel Radio Geometric Mean Algorithm for a Graph.
- Authors
ELrokh, Ashraf; Al-Shamiri, Mohammed M. Ali; Abd El-hay, Atef
- Abstract
Radio antennas switch signals in the form of radio waves using different frequency bands of the electromagnetic spectrum. To avoid interruption, each radio station is assigned a unique number. The channel assignment problem refers to this application. A radio geometric mean labeling of a connected graph G is an injective function h from the vertex set, V (G) to the set of natural numbers N such that for any two distinct vertices x and y of G , h (x) · h (y) ≥ d i a m + 1 − d (x , y) . The radio geometric mean number of h , r g m n (h) , is the maximum number assigned to any vertex of G. The radio geometric mean number of G, r g m n (G) is the minimum value of r g m n (h) , taken over all radio geometric mean labeling h of G . In this paper, we present two theorems for calculating the exact radio geometric mean number of paths and cycles. We also present a novel algorithm for determining the upper bound for the radio geometric mean number of a given graph. We verify that the upper bounds obtained from this algorithm coincide with the exact value of the radio geometric mean number for paths, cycles, stars, and bi-stars.
- Subjects
GRAPH algorithms; GRAPH labelings; RADIO antennas; INJECTIVE functions; NATURAL numbers; RADIO waves; RADIO technology
- Publication
Symmetry (20738994), 2023, Vol 15, Issue 3, p570
- ISSN
2073-8994
- Publication type
Article
- DOI
10.3390/sym15030570