Perfect roman domination in regular graphs
2018 ◽
Vol 12
(1)
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pp. 143-152
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Keyword(s):
A perfect Roman dominating function on a graph G is a function f : V (G) ? {0,1,2} satisfying the condition that every vertex u with f(u) = 0 is adjacent to exactly one vertex v for which f(v) = 2. The weight of a perfect Roman dominating function f is the sum of the weights of the vertices. The perfect Roman domination number of G, denoted ?pR(G), is the minimum weight of a perfect Roman dominating function in G. We show that if G is a cubic graph on n vertices, then ?pR(G) ? 3/4n, and this bound is best possible. Further, we show that if G is a k-regular graph on n vertices with k at least 4, then ?pR(G) ? (k2+k+3/k2+3k+1)n.
2020 ◽
Vol 12
(02)
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pp. 2050020
2018 ◽
Vol 11
(03)
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pp. 1850034
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2015 ◽
Vol 07
(04)
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pp. 1550048
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2019 ◽
Vol 13
(08)
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pp. 2050140
2020 ◽
Vol 39
(6)
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pp. 1381-1392
2016 ◽
Vol 10
(1)
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pp. 65-72
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