Title: Study of the crossing number associated with strong product of path with cycle and triangular snake graph

Authors: Mhaid Mhdi Alhajjar; Amaresh Chandra Panda; Siva Prasad Behera

Addresses: Department of Mathematics, C.V. Raman Global University, Bhubaneswar – 752054, India ' Department of Mathematics, C.V. Raman Global University, Bhubaneswar – 752054, India ' Department of Mathematics, C.V. Raman Global University, Bhubaneswar – 752054, India

Abstract: In 2018, Ouyang et al. presented the first efforts related to the crossing number of strong product of the path P_m to the cycle C_n. They proved that cr(P₂ ⊠ C_n) = n for n ≥ 3 together with introducing a general conjecture as follows: cr(P_m ⊠ C_n) = (m - 1)n: ∀ m, n ≥ 3. Here, we prove that Ouyang et al. conjecture is also true for n = 3 and m ≥ 3, together with exhibiting an optimal drawing of it. Furthermore, we start to study new case in relation to the strong product of path with triangular snake graph TS_n by proving that cr(P₂ ⊠ TS_n) = 3⌊n/2⌋ for n ≥ 3.

Keywords: crossing number; strong product; counting argument.

DOI: 10.1504/IJRIS.2025.147449

International Journal of Reasoning-based Intelligent Systems, 2025 Vol.17 No.3, pp.189 - 192

Received: 28 Apr 2023
Accepted: 29 May 2023
Published online: 16 Jul 2025 *

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