A NOTE ON LINE GRAPHS

Abstract

The line graph and 1-quasitotal graph are well-known concepts in graph theory. In Satyanarayana, Srinivasulu, and Syam Prasad [13], it is proved that if a graph G consists of exactly m connected components Gi 1 ≤ i ≤ m then L G = L G1 and L G1 is the ring sum of L G2 ,..., L Gm where L G denotes the line graph of G. In [13], the authors also introduced the concept 1-quasitotal graph and obtained that Q1 G is the ring sum of G and L G where Q1 G denotes 1-quasitotal graph of a given graph G. In this note, we consider zero divisor graph of a nite associate ring R and we will prove that the line graph of Kn-1 contains the complete graph on n vertices where n is the number of elements in the ring R.

Keywords

• line graph,quasi-total graph,zero-divisor graph,associate ring,complete graph.

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