Odd Hamming Distance Labeling of Some Path Related Graphs

Abstract

Binary data strings of equal length are compared using the metric called hamming distance. It is the number of bit positions in which the two binary strings differ. The hamming distance between two binary strings m and n of equal length is denoted by hd(m,n). We introduced the concept of Hamming distance labeling and odd Hamming distance labeling. In this paper, it is shown that Path graph, Star graph, One point union of Path graphs, Coconut tree, are Odd hamming distance labeled graphs and obtained their Odd hamming distance number. Both Hamming and Odd Hamming distance labeling are used to send secret messages in Cryptography.