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Generalization of Ramsey Number for Cycle with Pendant Edges

Author

Listed:
  • Jagjeet Jakhar

    (Department of Mathematics, Central University of Haryana, Jant-Pali, Mahendergarh 123031, India)

  • Monu Moun

    (Department of Mathematics, Central University of Haryana, Jant-Pali, Mahendergarh 123031, India)

  • Youngsoo Seol

    (Department of Mathematics, Dong-A University, Busan 49315, Republic of Korea)

  • Majeed Ahmad Yousif

    (Department of Mathematics, College of Education, University of Zakho, Zakho 42002, Iraq)

  • Muhammad Amer Latif

    (Department of Mathematics, College of Sciences, King Faisal University, Hofuf 31982, Saudi Arabia)

  • Pshtiwan Othman Mohammed

    (Department of Mathematics, College of Education, University of Sulaimani, Sulaymaniyah 46001, Iraq
    Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Rome, Italy
    Research and Development Center, University of Sulaimani, Sulaymaniyah 46001, Iraq)

Abstract

This paper explores various Ramsey numbers associated with cycles with pendant edges, including the classical Ramsey number, the star-critical Ramsey number, the Gallai–Ramsey number, and the star-critical Gallai–Ramsey number. These Ramsey numbers play a crucial role in combinatorial mathematics, determining the minimum number of vertices required to guarantee specific monochromatic substructures. We establish upper and lower bounds for each of these numbers, providing new insights into their behavior for cycles with pendant edges—graphs formed by attaching additional edges to one or more vertices of a cycle. The results presented contribute to the broader understanding of Ramsey theory and serve as a foundation for future research on generalized Ramsey numbers in complex graph structures.

Suggested Citation

  • Jagjeet Jakhar & Monu Moun & Youngsoo Seol & Majeed Ahmad Yousif & Muhammad Amer Latif & Pshtiwan Othman Mohammed, 2025. "Generalization of Ramsey Number for Cycle with Pendant Edges," Mathematics, MDPI, vol. 13(7), pages 1-21, April.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:7:p:1196-:d:1628351
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