Radio Antipodal Mean Number of Certain Graphs

D.Antony Xavier; R.C.Thivyarathi

doi:https://doi.org/10.14445/22315373/IJMTT-V54P556

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 54 | Number 6 | Year 2018 | Article Id. IJMTT-V54P556 | DOI : https://doi.org/10.14445/22315373/IJMTT-V54P556

Radio Antipodal Mean Number of Certain Graphs

D.Antony Xavier, R.C.Thivyarathi

Abstract

Let 𝐺 𝑉, 𝐸 be a graph with vertex set 𝑉 and edge set 𝐸. Let 𝑑 denote the diameter of 𝐺 and 𝑑 𝑢, 𝑣 denote the distance between the vertices 𝑢 and 𝑣in 𝐺. In this paper, we introduce a new labeling called radio antipodal mean labeling. An radio antipodal mean labeling of 𝐺 is a function 𝑓 that assigns to each vertex a non-negative integer such that 𝑓 𝑢 ≠ 𝑓 𝑣 if 𝑑 𝑢, 𝑣 < 𝑑and 𝑑 𝑢, 𝑣 + 𝑓 𝑢 +𝑓(𝑣) 2 ≥ 𝑑, for any two distinct vertices 𝑢, 𝑣 ∈ 𝑉(𝐺). The radio antipodal mean number of 𝑓 denoted by 𝑟𝑎𝑚𝑛 𝑓 , is the maximum number assigned to any vertex of 𝐺. The radio antipodal mean number of 𝐺, denoted by 𝑟𝑎𝑚𝑛 𝐺 is the minimum value of 𝑟𝑎𝑚𝑛 𝑓 taken over all radio antipodal mean labelings 𝑓 of 𝐺. We determine the antipodal mean number of path, circle, wheel, mesh and enhanced mesh.

Keywords

Labeling, radio antipodal mean numbering, diameter

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Citation :

D.Antony Xavier, R.C.Thivyarathi, "Radio Antipodal Mean Number of Certain Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 54, no. 6, pp. 467-470, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V54P556