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C24H18N6O7Na2, monoclinic, I2/a (no. 15), a = 9.9773(6) Å, b = 18.2319(14) Å, c = 14.2858(9) Å, β = 108.686(7)°, V = 2461.7(3) Å3, Z = 4, Rgt(F) = 0.0337, wRref(F2) = 0.0939, T = 200 K.

C12H14N4O4, triclinic, P1‾$P\overline{1}$ (no. 2), a = 6.79127(19) Å, b = 10.0328(3) Å, c = 10.0542(2) Å, α = 90.027(2)°, β = 97.124(2)°, γ = 101.983(3)°, V = 664.71(3) Å3, Z = 2, Rgt(F) = 0.0539, wRref(F2) = 0.1580, T = 292 K.

C36H42N4O10Mg, monoclinic, C2/c (no. 15), a = 16.4977(12) Å, b = 16.3866(10) Å, c = 12.5814(10) Å, β = 101.922(8)°, V = 3327.9(4) Å3, Z = 4, Rgt (F) = 0.0794, wRref (F 2) = 0.2021, T = 260 K.

Latin square, also known as Latin square matrix, refers to a kind of $ n\times n $ matrix, in which there are exactly $ n $ different symbols and each symbol appears exactly once in each row and column. A Latin square graph $ \Gamma(L) $ is a simple graph associated with a Latin square $ L $. This paper studied the relationships between the (total) Roman domination number and (total) domination number of Latin square graph $ \Gamma(L) $. We showed that $ \gamma_{R}(\Gamma(L)) = 2\gamma(\Gamma(L)) $ or $ \gamma_{R}(\Gamma(L)) = 2\gamma(\Gamma(L))-1 $, and $ \gamma_{tR}(\Gamma(L))\ge \frac{8\gamma_t(\Gamma(L))}{5} $ for $ n\ge 2 $. In 2021, Pahlavsay et al. proved $ \gamma(\Gamma(L))\ge \lceil \frac{n}{2}\rceil $ and $ \gamma_t(\Gamma(L))\ge \lceil \frac{4n-2}{7}\rceil $ for $ n\ge 2 $. In this paper, we showed that $ \gamma_R(\Gamma(L))\ge 2\lceil \frac{n}{2}\rceil $ (equality holds if, and only if, $ \gamma(\Gamma(L)) = \lceil \frac{n}{2}\rceil $) and $ \gamma_t(\Gamma(L)) > \frac{4n}{7} $ for $ n\ge 2 $. Since $ \gamma_R(G)\le 2\gamma(G) $ and $ \gamma_{tR}(G)\le 2\gamma_t(G) $ for any graph $ G $, our results can deduce or improve Pahlavsay et al.'s results. Moreover, we characterized these Latin squares for $ \gamma_R(\Gamma(L)) = 2\lceil \frac{n}{2}\rceil $, which is equal to $ \gamma(\Gamma(L)) = \lceil \frac{n}{2}\rceil $.

C22H23N3O9Cu, triclinic, P1‾$P\overline{1}$ (no. 2), a = 9.0356(2) Å, b = 9.6247(3) Å, c = 14.2969(3) Å, α = 86.989(2)°, β = 86.414(2)°, γ = 66.913(2)°, V = 1140.98(5) Å3, Z = 2, Rgt(F) = 0.0405, wRref(F2) = 0.1172, T = 297.88(10) K.

Let G=V,E be a simple graph. A subset D⊆V is a dominating set if every vertex not in D is adjacent to a vertex in D. The domination number of G, denoted by γG, is the smallest cardinality of a dominating set of G. The domination subdivision number sdγG of G is the minimum number of edges that must be subdivided (each edge can be subdivided at most once) in order to increase the domination number. In 2000, Haynes et al. showed that sdγG≤dGv+dGv−1 for any edge uv∈EG with dGu≥2 and dGv≥2 where G is a connected graph with order no less than 3. In this paper, we improve the above bound to sdγG≤dGu+dGv−NGu∩NGv−1, and furthermore, we show the decision problem for determining whether sdγG=1 is NP-hard. Moreover, we show some bounds or exact values for domination subdivision numbers of some graphs.

C23H17N3O5Cu, monoclinic, P21/n (no. 14), a = 11.49510(10) Å, b = 8.69660(10) Å, c = 21.1454(2) Å, β = 105.433(1)°, V = 2037.65(4) Å3, Z = 4, R gt(F) = 0.0298, wR ref(F 2) = 0.0862, T = 294 K.

C36H42N4O10Mg, monoclinic, C2/c (no. 15), a = 16.4977(12) Å, b = 16.3866(10) Å, c = 12.5814(10) Å, β = 101.922(8)°, V = 3327.9(4) Å3, Z = 4, Rgt(F) = 0.0794, wRref(F2) = 0.2021, T = 260 K. [ABSTRACT FROM AUTHOR]

C22H23N3O9Cu, triclinic, P 1 ‾ (no. 2), a = 9.0356(2) Å, b = 9.6247(3) Å, c = 14.2969(3) Å, α = 86.989(2)°, β = 86.414(2)°, γ = 66.913(2)°, V = 1140.98(5) Å3, Z = 2, Rgt(F) = 0.0405, wRref(F2) = 0.1172, T = 297.88(10) K. [ABSTRACT FROM AUTHOR]