id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
cana-4524	R. Sudhakar	Equitable Total Coloring of Line Graph of Certain Graphs	2025	10	.pdf	application/pdf	5136	190	75	3. Results and Discussion Theorem 3.1: Let ( )nL L represent the line graph of a ladder graph, then ( )'' ( ) 5.e nL L = Proof: Let    '( ( )) , :1 1 :1nV L L u v n u n   =   −   and    ' '' ' ''( ( )) , :1 2 , , , :1 1nE L L e f n e e f f n      =   −   − , where 1,e u u   += ' ' ,e u u  = '' ' 1,e u u   += 1,f v v   += ' ' ,f u v  = '' ' 1.f v u  += Theorem 3.2: Let ( )nL SL represent the line graph of a slanting ladder, then ( )'' ( ) 5.e nL SL = Proof: '( ( )) { , , :1 }nV L SL u v u n   =      ' '' ' ''( ( )) , :1 2 , , , :1 1nE L SL e f n e e f f n      =   −   − , where 1,e u u   += ' ' ,e u u  = ' ' ,e u u  = '' ' 1,e u u   +=	cache/cana-4524.pdf	txt/cana-4524.txt