id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
cana-3316	G. Navamani	Power Dominator Equitable Coloring for some Standard Graphs	2025	6	.pdf	application/pdf	3048	193	70	Set 𝑀1 contains 𝑚 vertices, while 𝑀2 contains 𝑛 number of vertices. Case 1: 𝑛 is even Let 𝐶2𝑘, 𝑘 ≥ 2 be an even cycle with the vertices 𝑎1, 𝑎2, … , 𝑎2𝑘, 𝑘 ≥ 2 and let 𝑎1𝑎2, 𝑎2𝑎3, … 𝑎2𝑘−1𝑎2𝑘, 𝑎2𝑘𝑎1 be the edges of 𝐶2𝑘. We assign color 1 to the vertices with the odd indices, i.e., to the vertices 𝑎2𝑗+1, 0 ≤ 𝑗 ≤ ⌊(2𝑘 − 1)/2⌋ and color 2 to the vertices with the even indices, i.e., to the vertices 𝑎2𝑗, 1 ≤ 𝑗 ≤ ⌊(2𝑘)/2⌋. Each vertex 𝑎𝑖, 1 ≤ 𝑖 ≤ 𝑛 power dominates all the Communications on Applied Nonlinear Analysis ISSN: 1074-133X Vol 32	cache/cana-3316.pdf	txt/cana-3316.txt