A NOTE ON LINE GRAPHS

S. BHAVANARI, S. DEVANABOINA, S. P. KUNCHAM

[PDF]

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.