Roman domination number of the join and corona of graphs

Authors

  • Lourdes Eullaran Mathematics Department, Negros Oriental State University, Dumaguete City, Philippines
  • Michael Baldado, Jr. Mathematics Department, Negros Oriental State University, Dumaguete City, Philippines

Keywords:

graph, dominating set, Roman dominating function, Roman nomination number, join, corona

Abstract

A Roman dominating function on a graph G=(V,E) is a function f:V(G)→{0,1,2} satisfying the condition that every vertex u for which f(u)=0 is adjacent to at least one vertex v for which f(v)=2. The weight of f is w(f)=∑v∈V f(v). The Roman domination number is the minimum weight of a Roman dominating function in G.

In this paper, a sharp upper bound of the Roman domination number of the join of two arbitrary graphs is given. In addition, the Roman domination number of the corona of two arbitrary graphs is also given.

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Published

2011-10-01

How to Cite

Eullaran, L., & Baldado, Jr., M. (2011). Roman domination number of the join and corona of graphs. The Mindanawan Journal of Mathematics, 2(1), 66–69. Retrieved from https://journals.msuiit.edu.ph/tmjm/article/view/20

Issue

Vol. 2 No. 1

Section

Articles