Total domination and vertex-edge domination in trees.

Resumen

A vertex v of a graph G = (V,E) is said to ve-dominate every edge incident to v, as well as every edge adjacent to these incident edges. A set S ⊆ V is a vertex-edge dominating set if every edge of E is ve-dominated by at least one vertex of S. The minimum cardinality of a vertex-edge dominating set of G is the vertex-edge domination number γve(G) . In this paper we prove (γt(T)−ℓ+1)/2 ≤ γve(T) ≤(γt(T)+ℓ−1)/2 and characterize trees attaining each of these bounds.

Biografía del autor

Venkatakrishnan Y. B., SASTRA Deemed University.
Department of Mathematics.
Naresh Kumar Hari, SASTRA Deemed University.
Department of Mathematics.
Natarajan Chidambaram, SASTRA Deemed University.
Department of Mathematics.

Citas

R. Boutrig, M. Chellali, T. W. Haynes and S. T. Hedetniemi, Vertexedge domination in graphs. Aequat. Math., 90, pp. 355—366, (2016).

M. A. Henning and A. Yeo, Total Domination in Graphs (Springer Monographs in Mathematics). 2013. ISBN: 978-1-4614-6524-9 (Print) 978-1-4614-6525-6 (Online).

B. Krishnakumari, Y. B. Venkatakrishnan and M. Krzywkowski, Bounds on the vertex-edge domination number of a tree. C. R. Acad. Sci. Paris, Ser.I 352, pp. 363—366, (2014).

J. R. Lewis, S. T. Hedetniemi, T. W. Haynes and G. H. Fricke, Vertexedge domination. Util. Math. 81, pp. 193—213, (2010).

J. W. Peters. Theoretical and algorithmic results on domination and connectivity. Ph.D. Thesis, Clemson University, (1986).

Publicado
2019-05-30
Cómo citar
[1]
V. Y. B., N. Hari, y N. Chidambaram, «Total domination and vertex-edge domination in trees»., PJM, vol. 38, n.º 2, pp. 295-304, may 2019.
Sección
Artículos