id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
iajs-3014	Shawkat, Noor K.; Ahmed, Mohammed A.	On Antimagic Labeling for Some Families of Graphs	2023	8	.pdf	application/pdf	3330	162	88	For the vertex-weights we get: 𝑤𝑡𝜇2 (𝑣1) = 𝜇2(𝑣1𝑣2) + 𝜇2(𝑣1𝑣𝑛) + 𝜇2(𝑣1𝑣𝑛+1) + 𝜇2(𝑣1𝑣2𝑛+1) + 𝜇2(𝑣1𝑣2𝑛) = (4𝑛 + 1) + (5𝑛) + 3 + 2 + 1 = 9𝑛 + 7, 𝑤𝑡𝜇2 (𝑣𝑖) = 𝜇2(𝑣𝑖𝑣𝑖+1) + 𝜇2(𝑣𝑖𝑣𝑖−1) + 𝜇2(𝑣𝑖𝑣𝑛+𝑖) + 𝜇2(𝑣𝑖𝑣2𝑛+1) + 𝜇2(𝑣𝑖𝑣𝑛+𝑖−1) for 𝑖 = 2, 3 … 𝑛 − 1, = (4𝑛 + 𝑖) + (4𝑛 − 1 + 𝑖) + (4𝑖 − 1) + (4𝑖 − 2) + (4𝑖 − 3) = 8𝑛 + 14𝑖 − 7 for 𝑖 = 2, 3, … , 𝑛 − 1, 𝑤𝑡𝜇2 (𝑣𝑛) = 𝜇2(𝑣𝑛𝑣1) + 𝜇2(𝑣𝑛𝑣𝑛−1) + 𝜇2(𝑣𝑛𝑣2𝑛) + 𝜇2(𝑣𝑛𝑣2𝑛+1) + 𝜇2(𝑣𝑛𝑣2𝑛−1) = (5𝑛) + (5𝑛 − 1) + (4𝑛 − 1) + (4𝑛 − 2) + (4𝑛 − 3) = 22𝑛 For the vertex-weights we get: 𝑤𝑡𝜇3 (𝑣1) = 𝜇3(𝑣1𝑣) + 𝜇3(𝑣1𝑣2) + 𝜇3(𝑣1𝑣𝑛+1) = 1 + 2 + 3 = 6, 𝑤𝑡𝜇3 (𝑣𝑖) = 𝜇3(𝑣𝑖𝑣) + 𝜇3(𝑣𝑖𝑣𝑖+1) + 𝜇3(𝑣𝑖𝑣𝑖−1) + 𝜇3(𝑣𝑖𝑣𝑛+𝑖−1) + 𝜇3(𝑣𝑖𝑣𝑛+𝑖) for 𝑖 = 2, 3 … , 𝑛 − 1, = (5𝑖 − 4) + (5𝑖 − 3) + (5𝑖 − 8) + (5𝑖 − 5) + (5𝑖 − 2) = 25𝑖	cache/iajs-3014.pdf	txt/iajs-3014.txt