A NOTE ON LINE GRAPHS

Abstract

The line graph and 1-quasitotal graph are well-known concepts in graphtheory.graph G consists of exactly m connected components Gi, 1im, then L(G) = L(G1) =L(G2) ? ... ? L(Gm) where L(G) denotes the line graph of G, and ? denotes the ringsum operation on graphs. In [13], the authors also introduced the concept 1-quasitotalgraph and obtained that Q1(G) = G ? L(G) where Q1(G) denotes 1-quasitotal graph ofa given graph G. In this note, we consider zero divisor graph of a finite associate ring Rand we will prove that the line graph of Kn-1contains the complete graph on n verticeswhere n is the number of elements in the ring R.