Common Multiples of Paths and Stars with Crowns

• Saritha Chandran C ^[1] ; T, Reji
  1. [1] Government Victoria College, Palakkad, Kerala, India-678001
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 43, Nº. 2, 2024, págs. 331-344
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • {\footnotesize A graph $G$ is a common multiple of two graphs $H_1$ and $H_2$ if there exists a decomposition of $G$ into edge-disjoint copies of $H_1$ and also a decomposition of $G$ into edge-disjoint copies of $H_2$. If $ G $ is a common multiple of $H_1$ and $H_2$, and $ G $ has $ q $ edges, then we call $ G $ a $ (q, H_1, H_2) $ graph. Our paper deals with the following question: Given two graphs $ H_1 $ and $ H_2$, for which values of $ q $ does there exist a $ (q, H_1, H_2) $ graph? when $H_1$ is either a path or a star with $3$ or $4$ edges and $H_2$ is a crown.}