Crossing Numbers of the Cartesian Product of the Double Triangular Snake Graphs With Path Pm.

Article Sidebar

pdf
Published: Dec 26, 2023
DOI: https://doi.org/10.53555/jaz.v44iS8.4099
Keywords:
Crossing number, Cartesian product, Join product, Double triangular snake graph, Path, cycle

Main Article Content

Pathak Manojkumar Vijaynath
Dr. Nithya Sai Narayana

Abstract

The crossing number Cr(G) of a graph G is the least number of edge crossings in all possible good drawings of G in the plane. Join and Cartesian products of graphs have many interesting graph-theoretical properties. In this paper, we evaluate the crossing number of the Cartesian product of double triangular snake graph DT2 with the path Pm. In this paper, we proved Cr(DT2 × Pm) = 6(m − 2), form ≥ 2 where Cr denotes the crossing number

Downloads

Download data is not yet available.

Article Details

How to Cite
Pathak Manojkumar Vijaynath, & Dr. Nithya Sai Narayana. (2023). Crossing Numbers of the Cartesian Product of the Double Triangular Snake Graphs With Path Pm. Journal of Advanced Zoology, 44(S8), 372–376. https://doi.org/10.53555/jaz.v44iS8.4099
Issue
Vol. 44 No. S8 (2023): Mathematics and Applied Sciences
Section
Articles
Creative Commons License

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

Author Biographies

Pathak Manojkumar Vijaynath

VPM’S Kannada high school and Junior college, Mithagar road, Mulund(E), Mumbai-81.

 

Dr. Nithya Sai Narayana

Department of Mathematics, University of Mumbai, Vidyanagari Kalina Santacruz East Mumbai-400098. narayana 

References

Bokal, D. On the crossing numbers of Cartesian products with paths. Journal of Combinatorial Theory, Series B 97, 3(2007),381–384.

Klesc, M.” The crossing numbers of products of paths and stars with 4-vertex graphs.” Journal of Graph Theory 18, 6(1994), 605–614.

Klesc, M.” The crossing numbers of cartesian products of paths with 5-vertex graphs”. Discrete Mathematics 233,1-3 (2001),353–359.

Maria´n Klesˇcˇ and stefan Schro¨tter,” THE CROSSING NUMBERS OF JOIN PRODUCTS OF PATHS WITH GRAPHS OF ORDERFOUR”. Discussiones Mathematicae Graph Theory 31(2)(2011) 321- 331.

Ouyang, Z., Wang, J., and Huang, Y. The crossing number of the Cartesian product of paths with complete graphs. Discrete Mathe- matics 328 (2014), 71–78.

Pathak Manojkumar Vijaynath and Dr. Nithya Sai Narayana” On the Crossing numbers of TSn × Pm and TSn × Cm.” Journal of Com- putational Mathematica (2023), 2456-8686.

Peng, Y., and Yiew, Y. The crossing number of p(3, 1) × Pn. Dis- crete mathematics 306, 16 (2006), 1941–1946.

Yiew, Y. C., Chia, G. L., and Ong, P.-H. Crossing number of the Cartesian product of prism and path. AKCE International Journal of Graphs and Combinatorics 0, 0 (2020), 1–7.

Yuan, Z., and Huang, Y. The crossing number of petersen graph P (4, 1) with paths Pn. Oper. Res. Trans 15, 3 (2011), 95–106.

Zheng, W., Lin, X., and Yang, Y. The crossing number of K2,m × Pn, Discrete Mathematics 308, 24 (2008), 6639–6644.