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

10 pages•Published: September 26, 2019

Sumonta Ghosh, Prakhar Pogde, Narayan C. Debnath and Anita Pal

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.

Keyphrases: cartesian product, complete bipartite graph, cycle, l(3 2 1) labeling, path

In: Quan Yuan, Yan Shi, Les Miller, Gordon Lee, Gongzhu Hu and Takaaki Goto (editors). Proceedings of 32nd International Conference on Computer Applications in Industry and Engineering, vol 63, pages 111-120.

Links:	https://easychair.org/publications/paper/whJ3
	https://doi.org/10.29007/x3qf

BibTeX entry

@inproceedings{CAINE2019:Efficient_Algorithm_L(3_2,
  author    = {Sumonta Ghosh and Prakhar Pogde and Narayan C. Debnath and Anita Pal},
  title     = {Efficient Algorithm For L(3,2,1)-Labeling of Cartesian Product Between Some Graphs},
  booktitle = {Proceedings of 32nd International Conference on Computer Applications in Industry and Engineering},
  editor    = {Quan Yuan and Yan Shi and Les Miller and Gordon Lee and Gongzhu Hu and Takaaki Goto},
  series    = {EPiC Series in Computing},
  volume    = {63},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/whJ3},
  doi       = {10.29007/x3qf},
  pages     = {111-120},
  year      = {2019}}

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