id author title date pages extension mime words sentence flesch summary cache txt cana-6025 R. Divinelin Kumari On the Chromatic Restrained Domination Number of Strong Product of Graphs 2024 10 .pdf application/pdf 4839 305 82 Thus, 𝐷1 is a chromatic restrained dominating set of πΎπ‘Ÿ ⊠ 𝑃𝑠 and π›Ύπ‘Ÿ 𝑐(πΎπ‘Ÿ ⊠ 𝑃𝑠) ≀ |𝐷1| = 𝑠 3 + 2π‘Ÿ βˆ’ 1 = π‘ βˆ’3 3 + 2π‘Ÿ = ⌈ π‘ βˆ’4 3 βŒ‰ + 2π‘Ÿ. Then, it remains to show that, π›Ύπ‘Ÿ 𝑐(πΎπ‘Ÿ ⊠ 𝑃𝑠) β‰₯ ⌈ π‘ βˆ’4 3 βŒ‰ + 2π‘Ÿ. Since, πœ’(πΎπ‘Ÿ ⊠ 𝑃𝑠) = 2π‘Ÿ Thus, we get a minimum chromatic restrained dominating set of πΎπ‘Ÿ ⊠ 𝑃𝑠 and π›Ύπ‘Ÿ 𝑐(πΎπ‘Ÿ ⊠ 𝑃𝑠) β‰₯ ⌈ π‘ βˆ’4 3 βŒ‰ + 2π‘Ÿ. Therefore, π›Ύπ‘Ÿ 𝑐(πΎπ‘Ÿ ⊠ 𝑃𝑠) = ⌈ π‘ βˆ’4 3 βŒ‰ + 2π‘Ÿ. Case (iii): 𝑠 ≑ 2(π‘šπ‘œπ‘‘ 3) cache/cana-6025.pdf txt/cana-6025.txt