The 2-Rainbow Domination Numbers of $${\boldsymbol{C}}_4\Box {\boldsymbol{C}}_n$$C4□Cn and $${\boldsymbol{C}}_8\Box {\boldsymbol{C}}_n$$C8□Cn
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DOI: 10.1007/s40009-018-0779-y
Abstract: A k-rainbow dominating function (kRDF) of G is a function $$f:V(G)\rightarrow {\mathcal {P}}(\{1,2,\ldots ,k\})$$f:V(G)→P({1,2,…,k}) for which $$f(v)=\emptyset $$f(v)=∅ we have $$\bigcup \nolimits _{u\in N(v)}f(u)=\{1,2,\ldots ,k\}$$⋃u∈N(v)f(u)={1,2,…,k}. The weightw(f) of a function f is defined as $$w(f)=\sum… read more here.
Keywords: boldsymbol box; box boldsymbol; boldsymbol; rainbow domination ... See more keywords
On 2-Rainbow Domination of Generalized Petersen Graphs P(ck,k)
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DOI: 10.3390/math11102271
Abstract: We obtain new results on the 2-rainbow domination number of generalized Petersen graphs P(ck,k). Exact values are established for all infinite families where the general lower bound 45ck is attained. In all other cases lower… read more here.
Keywords: rainbow domination; domination generalized; generalized petersen; petersen graphs ... See more keywords