International Journal of Mathematics Trends and Technology
Volume 69 | Issue 2 | Year 2023 | Article Id. IJMTT-V69I2P515 | DOI : https://doi.org/10.14445/22315373/IJMTT-V69I2P515
| Received | Revised | Accepted | Published |
|---|---|---|---|
| 07 Jan 2023 | 10 Feb 2023 | 21 Feb 2023 | 28 Feb 2023 |
For n 4, the cartesian product P3 × Cn is a polyhedral graph, where P3 is a 3-path and Cn is a n-cycle. A set H of disjoint even faces of P3 × Cn is called resonant pattern if P3 × Cn has a perfect matching M such that the boundary of every even face in H is M-alternating. Let k be a positive integer, P3 × Cn is k - resonant if any i k disjoint even faces of P3 × Cn form a resonant pattern. Moreover, if graph P3 × Cn is k - resonant for any integer k, then it is called maximally resonant. In this study, we provide a complete characterization for the k-resonance of P3 × Cn. We show that every graph P3 × Cn is 1- resonant, 2- resonant, 3- resonant and it is not k - resonant(k 4) except for P3 × C4, P3 × C6, P3 × C8. Moreover, we get a a corollary that P3 × Cn is maximally resonant if and only if it is 4-resonant.
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Yanfei Ma, Rui Yang, "k - Resonance of the Cartesian Product Graph P3 * Cn," International Journal of Mathematics Trends and Technology (IJMTT), vol. 69, no. 2, pp. 118-123, 2023. Crossref, https://doi.org/10.14445/22315373/IJMTT-V69I2P515
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