Even Hamming Distance Labeling of Some Path Related Graphs

Abstract

Hamming distance is used in error correction while transmitting data over computer networks.  In this paper, it is shown that Comb graph , Twig graph , Centipede  graph, and comb product of   and  graph  are even hamming distance labeled graphs. It is proved that the even hamming distance number of Comb graph and Twig graph are 6 and 8 respectively. Also the even hamming distance number of Centipede graph (m,2) is 6 if m=1 and 8 if  and for the comb product of  and  graph is 4 if  and 6 if  are obtained. This labeling is applied in Cryptography for sharing secret messages.