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(a, B)-Roman Domination On Cacti

Y. Zhao, H. Ahangar, Zuhua Liao, M. Chellali
Published 2017 · Computer Science

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Given two real numbers \(b\ge a>0\), an (a, b)-Roman dominating function on a graph \(G=(V,E)\) is a function \(f:V\rightarrow \{0,a,b\}\) satisfying the condition that every vertex v for which \(f(v)=0\) is adjacent to a vertex u for which \(f(u)=b\). In the present paper, we design a linear-time algorithm to produce a minimum (a, b)-Roman dominating function for cacti, a superclass of trees and different from chordal graphs.
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