2012
DOI: 10.37236/2595
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Abstract: Roman domination is an historically inspired variety of domination in graphs, in which vertices are assigned a value from the set $\{0,1,2\}$ in such a way that every vertex assigned the value 0 is adjacent to a vertex assigned the value 2. The Roman domination number is the minimum possible sum of all values in such an assignment. Using an algebraic approach we  present an $O(C)$-time algorithm for computing the Roman domination numbers of special classes of graphs called polygraphs, which include rotagraphs … Show more

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Cited by 38 publications
(53 citation statements)
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“…We begin with the second type. Particular dominating sets of P m ✷C n , with m ≥ n, based on regular patterns, give that (see [19]) However, the comparison with the exact values given in [8], for the cases 16 ≤ m ≤ 22, leads us to think that the construction shown in [19] for the case n = 5k is optimal, for m big enough (see Figure 2). Clearly this construction can be done for 5 ≤ n ≡ 0 (mod 5) and any m ≥ 2 and it provides a dominating set with (m+2)n 5 = (m + 2)k vertices.…”
Section: Known Bounds and Exact Valuesmentioning
confidence: 99%
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“…We begin with the second type. Particular dominating sets of P m ✷C n , with m ≥ n, based on regular patterns, give that (see [19]) However, the comparison with the exact values given in [8], for the cases 16 ≤ m ≤ 22, leads us to think that the construction shown in [19] for the case n = 5k is optimal, for m big enough (see Figure 2). Clearly this construction can be done for 5 ≤ n ≡ 0 (mod 5) and any m ≥ 2 and it provides a dominating set with (m+2)n 5 = (m + 2)k vertices.…”
Section: Known Bounds and Exact Valuesmentioning
confidence: 99%
“…In the case n ≡ 0 (mod 5), the construction provided in [19], that we have shown in Figure 2, of a dominating set of P m ✷C 5k with (m + 2)k vertices, is likely to be the optimal construction. If this is true, the lower bound of Equation 4 is not tight in this case and following this intuition, we have conjectured how a better general lower bound should be.…”
Section: Known Bounds and Exact Valuesmentioning
confidence: 99%
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