# (a, B)-Roman Domination On Cacti

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

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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