Line graph of unit graphs associated with finite commutative rings

• Pranjali ^[1] ; Kumar, Amit ^[2] ; Sharma, Pooja ^[2]
  1. [1] University of Rajasthan

     University of Rajasthan

     India

     
  2. [2] Banasthali Vidyapith.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 40, Nº. 4, 2021, págs. 919-926
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-4112
• Enlaces
  • Texto completo
• Resumen

  • For a given graph G, its line graph denoted by L(G) is a graph whose vertex set V (L(G)) = E(G) and {e1, e2} ∈ E(L(G)) if e1 and e2 are incident to a common vertex in G. Let R be a finite commutative ring with nonzero identity and G(R) denotes the unit graph associated with R. In this manuscript, we have studied the line graph L(G(R)) of unit graph G(R)  associated with R. In the course of the investigation, several basic properties, viz., diameter, girth, clique, and chromatic number of L(G(R)) have been determined. Further, we have derived sufficient conditions for L(G(R)) to be Planar and Hamiltonian

• Referencias bibliográficas
  • A. Kumar, Pranjali, M. Acharya, and P. Sharma, “Unit graphs having their domination number half their order,” in Recent advancements in graph...
  • N. Ashrafi, H. R. Maimani, M. R. Pournaki, and S. Yassemi, “Unit graphs associated with rings”, Communications in algebra, vol. 38, no. 8,...
  • R. P. Grimaldi, “Graphs from rings”, Congressus numerantium, vol. 71, pp. 95-103, 1990.
  • F. Harary, Graph theory. Reading, MA: Addison-Wesley, 1969.
  • N. Jacobson, Lectures in abstract algebra. New Delhi: East-West Press, 1951.
  • H. R. Maimani, M. R. Pournaki, and S. Yassemi, “Weakly perfect graphs arising from rings”, Glasgow mathematical journal, vol. 52, no. 3, pp....
  • Pranjali, "Graphs associated with commutative rings", Ph.D. Thesis, University of Delhi, Department of Mathematics, 2016.
  • Pranjali and M. Acharya, “Energy and Wiener index of unit graphs”, Applied mathematics & information sciences, vol. 9, no. 3, pp. 1339-1343,...