Efficient Algorithm For L(3,2,1)-Labeling of Cartesian Product Between Some Graphs

Abstract

L(h,k) Labeling in graph came into existence as a solution to frequency assignment problem. To reduce interference a frequency in the form of non negative integers is assigned to each radio or TV transmitters located at various places. After L(h,k) labeling, L(h,k, j) labeling is introduced to reduce noise in the communication network. We investigated the graph obtained by Cartesian Product betweenCompleteBipartiteGraphwithPathandCycle,i. e.,Km,n×Pr andKm,n×Cr byapplying L(3,2,1)Labeling. The L(3,2,1) Labeling of a graph G is the difference between the highest and the lowest labels used in L(3,2,1) and is denoted by λ3,2,1(G) In this paper we have designed three suitable algorithms to label the graphs Km,n × Pr and Km,n × Cr . We have also analyzed the time complexity of each algorithm with illustration.