Topological Hoarded Graphs

Topological Hoarded Graphs

In this paper, we first introduced the steps to be taken to get the set-family corresponding to a hoarded graph, and an example implementation of these steps. We then give the notion of topological hoarded graph and show when a set-family induced by a topological hoarded graph is a topology on a set. We also present some useful facts about topological hoarded graphs.

___

  • B. Bollobas, Modern Graph Theory. New York, NY: Springer, 2014.
  • G. Chartrand, A First Course in Graph Theory. Mineola, NY: Dover Publications, 2012.
  • J. L. Gross, J. Yellen, and P. Zhang, Eds., Handbook of graph theory, second edition, 2nd ed. London, England: CRC Press, 2018.
  • K. Polat, “On cumulative graph representations of set-families,” Karamanoğlu Mehmetbey Üniversitesi Mühendislik ve Doğa Bilimleri Dergisi, vol. 3, no. 2, pp. 74–78, 2022.
  • K. S. Htay, K. A. Tint, and N. O. Htike, “Application of connectivity on graph theory,” International Journal of Scientific Engineering and Technology Research, vol. 8, no. 1, pp. 525–530, 2019.
  • K. R. Saoub, Graph theory: An introduction to proofs, algorithms, and applications. London, England: CRC Press, 2021.
  • R. J. Trudeau, Introduction to graph theory. Pmapublishing.com, 2017.