id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
cana-4517	Prema M	A Study on Perfect Rings Dominating Energy of Graphs	2025	9	.pdf	application/pdf	3562	246	86	[λ4 − 2λ3 − (pq − 1)λ2 + (2pq − (p + q))λ − [pq − (p + q) + 1]] ≈ λp+q−4(λ − 1)[λ3 − λ2 − pqλ − (pq− (p + q))] φ(Kp,q, λ) ≈ λ p+q−4(λ − 1)2(λ2 − pq) iii) Suppose p > q, then the PRD matrix is of the form 𝔓A(Kp,q) = ( P Q R S ) where P = ( 1 O1×p−1 Op−1×1 Op−1 ); Q = (Jp×q) R = (Jq×p); S = ( 1 O1×q−1 Oq−1×1 Oq−1 ) here J and O represents the matrix of 1’s and 0’s. = (2p − 3)|−1| + |p − 1| + | p + √(p − 2)2 + 8 2 | + | p − √(p − 2)2 + 8 2 | Thus, 𝔓𝔈A(Bp,p)	cache/cana-4517.pdf	txt/cana-4517.txt