Title of article :
a note on roman k-tuple domination number
Author/Authors :
abd aziz, noor a lawiah universiti sains malaysia - school of mathematical sciences, penang, malaysia , jafari rad, nader shahed university - department of mathematics, tehran, iran
Abstract :
for an integer k≥2, a roman k-tuple dominating function, (or just rkdf), in a graph g 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 k vertices v for which f(v)=2, and every vertex u for which f(u)≠0 is adjacent to at least k−1 vertices v for which f(v)=2. the roman k-tuple domination number of g is the minimum weight of an rkdf in g. in this note we settle two problems posed in [roman k-tuple domination in graphs, iranian j. math. sci. inform. 15 (2020), 101--115].
Keywords :
roman domination, total roman domination , roman k , tuple domination
Journal title :
Communications in Combinatorics and Optimization
Journal title :
Communications in Combinatorics and Optimization
