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Concepts on Coloring of Cluster Hypergraphs with Application

Author

Listed:
  • Sovan Samanta
  • Jeong Gon Lee
  • Usman Naseem
  • Shah Khalid Khan
  • Kousik Das

Abstract

Coloring of graph theory is widely used in different fields like the map coloring, traffic light problems, etc. Hypergraphs are an extension of graph theory where edges contain single or multiple vertices. This study analyzes cluster hypergraphs where cluster vertices too contain simple vertices. Coloring of cluster networks where composite/cluster vertices exist is done using the concept of coloring of cluster hypergraphs. Proper coloring and strong coloring of cluster hypergraphs have been defined. Along with these, local coloring in cluster hypergraphs is also provided. Such a cluster network, COVID19 affected network, is assumed and colored to visualize the affected regions properly.

Suggested Citation

  • Sovan Samanta & Jeong Gon Lee & Usman Naseem & Shah Khalid Khan & Kousik Das, 2020. "Concepts on Coloring of Cluster Hypergraphs with Application," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-10, August.
    • Handle: RePEc:hin:jnlmpe:3705156
    DOI: 10.1155/2020/3705156
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