Root square mean labeling of arrow graphs with encoding and decoding

Abstract

A graph G with p vertices and q edges is called a Root Square mean labeling if it is possible to label the vertices x ∈ v with distinct labels ρ(x) from 1, 2, · · · , q + 1 in such a way that each edge e = ab is labeled with ρ = √ρ(a)²+ρ(b)²/2 or √ρ(a)2+ρ(b)22 then the edge labels are distinct. In this case ρ is called Root Square mean(RSM) labeling of G . In this paper we prove Arrow graphs A2n,A3n,A4n admits Root Square mean (RSM) labeling.In today’s world, digital data transfer is becoming more and more common in all industries. Data security plays a critical role in the delivery and storage of data. Labeling is an essential component of the cryptosystem. A new approach in the encoding and decoding process on the Root Square Mean Labeling is applied in this paper through an algorithm for encoding and decoding of secured message.