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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.39 no.6 Antofagasta Dec. 2020

http://dx.doi.org/10.22199/issn.0717-6279-2020-06-0084 

Artículos

Trees with vertex-edge roman domination number twice the domination number minus one

1SASTRA University, Dept. of Mathematics, School of Arts, Science and Humanities, Tanjore, TN, India. e-mail: nareshhari1403@gmail.com

2SASTRA University, Dept. of Mathematics, School of Arts, Science and Humanities, Tanjore, TN, India. e-mail: venkatakrish2@maths.sastra.edu

Abstract

A vertex-edge Roman dominating function (or just ve-RDF) of a graph G = (V, E) is a function f : V (G) → {0, 1, 2} such that for each edge e = uv either max{f (u), f (v)} ≠ 0 or there exists a vertex w such that either wu ∈ E or wv ∈ E and f (w) = 2. The weight of a ve-RDF is the sum of its function values over all vertices. The vertex-edge Roman domination number of a graph G, denoted by γ veR (G), is the minimum weight of a ve-RDF G. We characterize trees with vertexedge roman domination number equal to twice domination number minus one.

Keywords: Vertex-edge roman dominating set; Dominating set; Trees

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Acknowledgement:

The second author thanks DST SERB(MATRICS)- grant number MTR/2018/000234 for the support.

References

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Received: May 31, 2019; Accepted: September 30, 2020

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