Covering of Line Graph of Zero Divisor Graph over Ring Zn
Sheela Suthar *
Department of Mathematics and Statistics, Banasthali Vidyapith, Banasthali- 304 022, Rajasthan, India.
Om Prakash
Department of Mathematics, IIT Patna, Patliputra colony, Patna-800 013, India.
*Author to whom correspondence should be addressed.
Abstract
Let Zn be the commutative ring of residue classes modulo n, Γ(Zn) the zero divisor graph of
Zn and L(Γ(Zn) be the line graph of Γ(Zn). We have studied the point covering number and
independence number of L(Γ(Zn)), for some positive integer n. We have computed edge covering
number for L(Γ(Zpq), and establish the relation among point covering, independence number and
edge covering number of L(Γ(Zpq), where p and q are prime numbers.
Keywords: Commutative Ring, Zero Divisor Graph, Line Graph, Point Covering, Independence Number, Edge Covering.