Revista Integración, temas de matemáticas.

Revista Integración, temas de matemáticas

Vol. 40 No. 1 (2022): Revista Integración, temas de matemáticas
Research and Innovation Articles

A new sum of graphs and caterpillar trees

PDF
N. B. Huamaní
Universidad Nacional de San Cristóbal de Huamanga
Joice S. do Nascimento
Univerdidade do Estado do Rio de Janeiro,
A. Condori
Universidad Nacional de San Cristóbal de Huamanga
DOI: https://doi.org/10.18273/revint.v40n1-2022004

Published 2022-03-01

Keywords

  • Graph,
  • Caterpillar trees,
  • tree graphs,
  • sum of graphs

How to Cite

Berrocal Huamaní, N. ., Santos do Nascimento, J., & Condori Huamán, A. P. (2022). A new sum of graphs and caterpillar trees. Revista Integración, Temas De matemáticas, 40(1), 77–85. https://doi.org/10.18273/revint.v40n1-2022004

Copyright (c) 2022 Revista Integración, temas de matemáticas

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Caterpillar trees, or simply Caterpillar, are trees such that when we remove all their leaves (or end edge) we obtain a path. The number of nonisomorphic caterpillars with n ≥ 2 edges is 2n−3 + 2⌊(n−3)/2⌋. Using a new sum of graphs, introduced in this paper, we provided a new proof of this result.

PDF

Downloads

Download data is not yet available.

References

  1. Frank H. and Schwenk A.J., “The number of caterpillars”, Discrete Mathematics, 6 (1973), No. 4, 359-365. doi:10.1016/0012-365X(73)90067-8.
  2. Hacon D., Mendes de Jesus C. and Romero Fuster M.C., “Stable maps from surfaces to the plane with prescribed branching data”, Topology and Its Appl., 154 (2007), No. 1, 166-175. doi:10.1016/j.topol.2006.04.005.
  3. Huamaní N. B., Mendes de Jesus C. and Palacios J., “Invariants of stable maps from the 3-sphere to the Euclidean 3-space”, Bull Braz Math Soc, New Series, 50 (2019), 913–932. doi:10.1007/s00574-019-00133-4.
  4. Huamaní N. B. and Mendes de Jesus C., “Grafos pesados y aplicaciones estables de 3-variedades en R3”, Rev. Integr. temas mat., 39 (2021), No. 1, 109-128. doi:10.18273/revint.v39n1-2021008.