id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-5569	NourEldeen, Nawal M.; Badr, Elsayed; Shabana, Hanan; Abdel-Aal, M. E.	Upper Bound of Radio Span for Shadow-path Network and Its Mathematical Modeling	2025	25	.pdf	application/pdf	9457	547	85	[(n+ 2) + (2n+ 7)(k − 2) + 2(k − 2)(k − 3)+ + (2n+ 1) + (n+ 1)(k − 1) + 2(k − 1)(k − 2)]| = |(2n+ 7)(k − 1) + 2(k − 2)(k − 3) + (2n+ 1) + (n+ 1)(k − 1)+ + 2(k − 1)(k − 2)| ≥ n, where n = 4k, d(x, y) ≥ 1 ≥ diam(D2(Pn)) + 1− d(x, y) case 9If {x, y} = {v1, v3k−1} then |f(x)− f(y)| = |f(v1)−	cache/ejpam-5569.pdf	txt/ejpam-5569.txt