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Locating-Total Domination Number of Cacti Graphs

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Listed:
  • Jianxin Wei
  • Uzma Ahmad
  • Saira Hameed
  • Javaria Hanif

Abstract

For a connected graph J , a subset is termed as a locating-total dominating set if for , and for . The number of elements in a smallest such subset is termed as the locating-total domination number of J . In this paper, the locating-total domination number of unicyclic graphs and bicyclic graphs are studied and their bounds are presented. Then, by using these bounds, an upper bound for cacti graphs in terms of their order and number of cycles is estimated. Moreover, the exact values of this domination variant for some families of cacti graphs including tadpole graphs and rooted products are also determined.

Suggested Citation

  • Jianxin Wei & Uzma Ahmad & Saira Hameed & Javaria Hanif, 2020. "Locating-Total Domination Number of Cacti Graphs," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-10, October.
    • Handle: RePEc:hin:jnlmpe:6197065
    DOI: 10.1155/2020/6197065
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