On Radio Geometric Mean 𝐷- Distance Number of
Some Basic Graphs

K. John Bosco; S. Priya

doi:https://doi.org/10.14445/22315373/IJMTT-V67I2P514

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 67 | Issue 2 | Year 2021 | Article Id. IJMTT-V67I2P514 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I2P514

On Radio Geometric Mean 𝐷- Distance Number of Some Basic Graphs

K. John Bosco, S. Priya

Abstract

A Radio geometric mean 𝐷-distance labeling of a connect graph 𝐺 is an injective function 𝑓 from the vertex set 𝑉(𝐺) to the ℕ such that for two distinct vertices 𝑢 and 𝑣 of 𝐺, 𝑑 𝐷(𝑢, 𝑣) + ⌈√𝑓(𝑢)𝑓(𝑣) ⌉ ≥ 1 + 𝑑𝑖𝑎𝑚𝐷(𝐺), 𝑤ℎ𝑒𝑟𝑒 𝑑 𝐷(𝑢, 𝑣) denotes the 𝐷-distance between 𝑢 and 𝑣 𝑑𝑎𝑖𝑚𝐷(𝐺) denotes the 𝐷-diameter of 𝐺. The radio geometric mean 𝐷-distance number of 𝑓, 𝑟𝑔𝑚𝑛𝐷(𝑓) is the maximum label assigned to any vertex of 𝐺 . The radio geometric mean 𝐷-distance number of, 𝑟𝑔𝑚𝑛𝐷(𝐺)is the minimum value of 𝐺, 𝑟𝑔𝑚𝑛𝐷(𝐺) is the minimum value of 𝑟𝑔𝑚𝑛𝐷 (𝑓) taken over all radio geometric mean 𝐷-distance labeling 𝑓 of 𝐺. In this paper we find the radio geometric mean 𝐷-distance number of some basic graphs.

Keywords

𝐷-distance, Radio geometric mean 𝐷-distance, Radio geometric mean 𝐷-distance number.

References

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Citation :

K. John Bosco, S. Priya, "On Radio Geometric Mean 𝐷- Distance Number of Some Basic Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 2, pp. 103-108, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I2P514