A note on line graphs
Citation
Satyanarayana, B., Srinivasulu, D. & Syam Prasad, K. (2017). A note on line graphs. TWMS Journal Of Applied And Engineering Mathematics, 7(1), 173179.Abstract
The line graph and 1quasitotal graph are wellknown 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) = L(G2) ⊕ ... ⊕ L(Gm) where L(G) denotes the line graph of G, and ⊕ denotes the ring sum operation on graphs. In [13], the authors also introduced the concept 1 quasitotal graph and obtained that Q1(G) = G⊕L(G) where Q1(G) denotes 1quasitotal graph of a given graph G. In this note, we consider zero divisor graph of a finite 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.
Source
TWMS Journal Of Applied And Engineering MathematicsVolume
7Issue
1URI
https://hdl.handle.net/11729/2621http://jaem.isikun.edu.tr/web/index.php/archive/93vol7no1/290anoteonlinegraphs
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