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- W65640090 abstract "An edge-colored graph G is rainbow connected if any two vertices are connected by a path whose edges have distinct colors. The rainbow connection number of a connected graph G, denoted by rc(G), is the smallest number of colors that are needed in order to make G rainbow connected. In this paper, we investigate rainbow connection numbers of three subfamilies of undirected double-loop networks, denoted by rc(G(n; ±s 1, ±s 2)), where 1 ≤ s 1 < s 2 < n∕2. We almost determine the precise value for the case that $$s_{1} = 1,s_{2} = 2$$ . For the case that $$n = ks,s_{1} = 1,s_{2} = s$$ , where s ≥ 3 and k ≥ 1 are integers, we derive that $$rc(G(ks;pm 1,pm s)) leq min {lceil frac{k} {2} rceil + s,lceil frac{s+1} {2} rceil + k - 1}$$ . For the case that $$n = 2ks,s_{1} = 2,s_{2} = s$$ , where k ≥ 1 are integers and s ≥ 3 are odd integers, we have $$rc(G(n;pm s_{1},pm s_{2})) leq lceil frac{ks} {2} rceil + k$$ ." @default.
- W65640090 created "2016-06-24" @default.
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- W65640090 date "2014-10-15" @default.
- W65640090 modified "2023-10-03" @default.
- W65640090 title "Rainbow Connection Numbers for Undirected Double-Loop Networks" @default.
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- W65640090 doi "https://doi.org/10.1007/978-3-319-08377-3_12" @default.
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