Vertex cover and Edge vertex domination in trees

• Senthilkumar, B. ^[1] ; Naresh Kumar, H. ^[1] ; Venkatakrishnan, Y. B. ^[1]
  1. [1] SASTRA Deemed University.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 40, Nº. 5, 2021, págs. 1147-1154
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-3532
• Enlaces
  • Texto completo
• Resumen

  • Let G = (V,E) be a simple graph. An edge e ∈ E(G) edge-vertex dominates a vertex v ∈ V (G) if e is incident with v or e is incident with a vertex adjacent to v. A subset D ⊆ E(G) is an edge-vertex dominating set of a graph G if every vertex of G is edge-vertex dominated by an edge of D. A vertex cover of G is a set C ⊆ V such that for each edge uv ∈ E at least one of u and v is in C. We characterize trees with edge-vertex domination number equals vertex covering number.

• Referencias bibliográficas
  • R. Dutton and W. F. Klostermeyer, “Edge dominating sets and Vertex Covers”, Discussiones Mathematicae Graph Theory, vol. 33, pp. 437-456,...
  • W. F. Klostermeyer, M. E. Messinger and A. Yeo, “Dominating Vertex Covers: The Vertex-Edge Domination Problem”, Discussiones Mathematicae...
  • B. Krishnakumari, Y. B. Venkatakrishnan and M. Krzywkowski, “On trees with total domination number equal to edge-vertex domination number...
  • J. R. Lewis, "Vertex-edge and edge-vertex parameters in graphs", Ph. D. Thesis, Clemson University, 2007.
  • K. W. Peters, “Theoretical and Algorithmic Results on Domination and Connectivity”, Ph.D. Thesis, Clemson University, 1986.
  • Y. B. Venkatakrishnan and B. Krishnakumari, “An improved upper bound of edge-vertex domination number of a tree”, Information Processing Letters,...